GA IFR pilot reported a flight in heavy IMC conditions. The 328 hour pilot with little IFR experience reported heading deviations; altitude deviations and slow reaction time to changing weather conditions.

Narrative

I am a fairly new 350 hour instrument rated private pilot in this airplane.This flight; a short 20 minute return flight; at dusk in moderate precipitation and light to moderate icing; started with a failure to activate vectors to final and blowing through the final approach course for an ILS; which then went into some challenges in maintaining heading and altitude while being vectored in hard IMC; in what felt like un-commanded roll due to possible icing; but also could have just been poor piloting. The initial buttonology failure in the avionics came from unfamiliarity and an ill-advised and ill-timed change in habit.My training was to always load the approach with an initial fix; and then activate the leg if vectored in; the smart logic being that ATC could always send you out to a fix. But this was a short flight over some mountains with expected light icing; and ATC let me know I'd be getting vectors early in the flight before I had loaded the approach or even gotten the weather. I was pointed right at the final approach course; was already feeling behind since I had just completed the departure procedure and needed weather and brief the approach; and was in moderate icing and fixated a bit on the wing; looking for ice. So I went ahead and chose vectors instead of an initial fix when loading the approach while also requesting lower from 6;000 ft.; hoping to descend out of the icing layer. I didn't know which fix would even make sense since I hadn't briefed the approach; so that just seemed faster. That should have immediately followed with activate vectors to final procedure to turn the entire final into an intercept magenta line to get the approach out of standby; but I didn't do this; and it somehow didn't occur to me that I needed to activate the leg. I got the weather; briefed the approach; I had it in my mind that if I activated the approach with the APR button; as soon as I got clearance; that activating the approach would do three things; 1- arm the glideslope; 2- activate vectors to final; and 3- intercept the final approach course. In hindsight; that seems so basic and obvious that I skipped a step and that the plane wasn't going to intercept a leg that hadn't been activated to be next in sequence. It had been four months since an IPC; which didn't include any vectors to final; and 10 months since my IFR checkride; and was just enough nuanced from my normal practice of loading a fix that I wasn't sharp enough or proficient enough to have caught my mistake. I could see in the scoreboard that I was still direct to the initial VOR I was pointed at before switching to heading mode to the assigned heading; so there was a slight spidey tingle; but I just thought APR would arm everything and bring up the green needles; some expectation bias.I probably could have corrected quickly by matching my heading to the final; activating vectors to final; I was still within the final approach corridor. But I chose to completely turn off the automation and disconnect; which is probably the right thing to do in many circumstances; but maybe wasn't the most helpful step in this case; where the rain was pouring down; the ice was mostly cleared from the wings from the high mode; not max mode; TKS; skirting right at freezing level. ATC inquired if I was established; and I let the controller know; which I figured they could probably see; that I had blown through final. As I recall; I was on a heading of about 120 and was given a right heading of 300 degrees. The correction of completely disengaging the Autopilot was compounded by what I believe was ice impacted ailerons and possibly elevator impacting roll and pitch control in the subsequent attempt to get vectored back to the ILS; because I found each turn to be going into a bigger roll than expected with a quick loss of altitude.Again; I was running my TKS in high; but not boost mode; and it looked to have sloughed the light to moderate icing that I could see accumulated;but the plane definitely was not handling as crisply as I had ever experienced and I was; no other way to put it; frazzled. The plane was banking to about 45 degrees; dropping altitude at over 2000 fpm; and I would bring it back and try and ascend and on the next turn; same thing; more roll; altitude drop; with a resulting reacting over correction. I think this happened at least 4 times; and two 360's to rejoin the final; with clearly concerned controllers. I could see I had gotten to about 1500 ft. AGL; so knew I had gone below the MVA/MEA.While I believe the controls may not have been responding quite as usual due to some wing contamination; I also recognize that it was me at the controls and I was not maintaining the control necessary to fly the assigned heading and altitudes. They say lizard brain steps in and your arms get shorter; and I was literally shocked with each turn that I was not holding altitude and banking; and was certainly task saturated loading headings; talking to ATC; trying to maintain situational awareness; checking wings for icing; but I knew I was now flying by the seat of my pants. Power inputs felt late; corrections were too strong; attempts to get back onto Autopilot were clumsy; there was nothing pretty about the flying I was doing.I have to accept that in that moment; I was only ready for things to go right; and soon as I made a buttonology mistake; and as soon as I was hand flying in IMC with the next steps not already loaded; my controls of the plane were crude at best and my instrument scan not brisk and systematic enough. Single pilot IFR is no joke. The conditions at my intended airport were MVFR with I think ceilings of about 2;300 ft.; but the floor of the icing layer; approximately 2;800 ft.; was above the MVA/MEA of 4;500 ft.; which meant I didn't have an out to get below the icing without [requesting priority handling] and taking terrain risk into my own hands. I knew I had plenty of TKS for the short flight with no severe icing forecast; but I did hit a very heavy; to me; precipitation cell; and that added to the IMC experience.I feel obligated to read most accident reports; and probably most people reading this one can sense a few other factors. They say mountains; night; IMC; pick one. I transferred some of my luck bucket to the experience bucket; and cannot say that my ADM is what it needed to be; or that my instrument flying skills were where they need to be; so lots of take aways. The ones I've got are:1) Get weekly avionics practice2) In hard IMC; maybe consider small step downs in automation without complete step off; or at least be very prepared with a flow to get back on if nothing more than heading and alt select.3) Force a rigorous instrument scan cycle; it took a few seconds to figure out the roll and descent each time; and should have been babying the plane into each turn.4) Get real or simulated hard IMC practice with an instructor regularly to practice just these scenarios.5) Don't plan a flight with known icing where you cannot have ATC descend you below the icing layer.6) Talk to ATC to buy some time with a delay vector to get back set up.Thanks for reading and hope this helps someone avoid finding themselves in a similar situation because it was an uncomfortable sequence.