Denver TRACON Controller reported Denver Center was not following the LOA which caused an aircraft to possibly enter airspace without being pointed out; and was also involved in an aircraft conflict.

Narrative

XA:09Z: Aircraft X tags up descending out of FL335; DR2/1N accepts the hand off; expecting a coordination from ZDV Sector 27. None occurs.XA:11z: Aircraft X crosses the ZDV/D01 lateral boundary at FL310.Aircraft X checks in with DR2 given the route DANDD..GXY from ZDV and descending to 12;000 feet. According to the ZDV/D01 LOA; GXY arrivals are to be assigned DANDD1 Arrival and level at FL230. While Aircraft X continued descending from FL310; they transitioned through ZDV Sector 7 airspace with the DR2 controller unsure of point out status. There were two departures climbing via SID off DEN eastbound that were no longer ensured separation with Aircraft X because of the descent clearance to 12;000 feet. Aircraft X was stopped at 17;000 and vectored heading 300 to avoid DEN departures and arrivals. No LOSS occurred; however due to the nonstandard routing and clearance to descend into D01 airspace from ZDV Sector 27; airspace; procedures and safety were all compromised.ZDV regularly shows a blatant disregard for 7110.65 and LOA procedures and no action seems to ever be taken from their management to address deficiencies in performance. D01 controllers are regularly put in the position of having to accept aircraft; in violation with LOA routings with no coordination. D01 is often expected to fix ZDV's mistakes; which regularly leads to unsafe situations within D01 airspace that could have been resolved miles outside of our boundary.