Center Controller reported deteriorating weather conditions resulted in several aircraft going through the weather; others having to deviate off flight plan; and three NMACs.

Narrative

Weather was building through out sector A; there was only one way through and that was over ZZZ VOR. I told Sector B; to the west; to not send aircraft south; there was no hole. So they sent 6 down south; the pilots on frequency said no: they wanted to go north; Sector B forced them south into weather; when I got them they didn't know what to do; they were forced to go through moderate and heavy weather and to avoid the worst of it deviate nearly 200 miles off their flight plan into MMTY airspace; 2 became conflictions with their traffic that required even more attention: every aircraft had to be put on vectors to go through the smallest gaps I could find. Up north they were getting through a gap just fine; no reason to send south; my coworkers on Sector B ignored my instructions; added complexity; screwed me over. While these 6 aircraft needed extreme hand holding through the weather; the frequency test on 135.87; Sector C; using it as the primary sector became a huge issue. Primarily because the radio was not reaching the aircraft because of weather conditions; this was noted to management and the 2 in charge of the test long prior; and ignored. As a result; a Company aircraft at FL300 could not hear my calls to climb because of the congestion from smaller aircraft wanting to depart; those VFR's wanting flight following and the 6 before mentioned aircraft that could not hear me because of the other transmitter I was using and the frequency kept getting blocked up. The result was I had to use guard to climb the aircraft; turn them hard to the left and use the word immediately for only the 2nd time in 2 years of ATC. Then after the numbers were peaking; with a D side they finally decided to split the sector after having asked for about an hour. Problem with that is the frequency we were using is 135.87; the low sector's frequency. SO when the split happened; ALL AIRCRAFT were on the low frequency and not on A; so with weather deviations numbering about 15 aircraft (on vectors because of restricted airspace; other traffic situations) we had to figure out which frequency the aircraft were on. Again; this had been mentioned long before as a nightmare scenario that was going to cause incidents to happen; and problems to arise. It happened in the form of an aircraft getting lost on the frequency switch and was traffic for someone coming from ZFW; luckily he showed up on INK's frequency and they were able to advert the incident. The other incident was with an aircraft deviating north of CNM; that got west toward the WILEY airspace (plan was to turn them south and vector around because of the only gap we had. That aircraft was on 135.87; out of sector's C's boundary but left on their frequency; during the brief from my D side; he was forgotten or lost and Sector E had to alert us to the impending airspace violation. My last count was 4 airspace potential violations; Sector 3 barely avoided NMAC's with climbers and descenders; and too many missed PO's to Sector E to even count. Primarily because of the frequency test and the subsequent split and confusion associated with this frequency configuration. I'm going to say supervisor neglect because the sector should have been split about an hour before; lack of staffing; TMU during all this tried to give us T routes for ZFW; we were allot busier then they were considering the weather deviations were in my airspace not ZFW. General lack of concern from surrounding sectors at ZAB; not routing around weather; not allowing aircraft to deviate and not controlling the aircraft where I needed them to go all played a major factor in this being the worst weather event of my 22 year career. There are not words to describe how terrible this could have gone; and the growing concern of mine that from the top down there is a general lack of care about aircraft safety at ZAB. Stop the 135.87 immediately; disband TMU from making decisions about T routes; take away their ability to help and add structure.Allow TMU to issue routes around the weather; the playbooks seem to only hurt; the structure added only seems to hurt the safety of the NAS.