I understand your frustration; the grid works in a way you wouldn't expect. Part of the fun is figuring out the rules through experimentation, but if you're struggling, here's what I've found, in rot13.
Generally:
Gur angher bs gur tevq vfa'g cresrpgyl gevnathyne. Lbh pna guvax bs vg nf n 4-qverpgvbany tevq cerfragrq va na hapbairagvbany jnl naq jvgu fcrpvny ehyrf onfrq ba rnpu fcnpr'f bevragngvba (gung vf, jurgure gur gevnatyr cbvagf hc be qbja). Fcnprf nygreangr orgjrra hc naq qbja va n purpxreobneq funcr. Rirelguvat zbirf npebff gur tevq yvarf, arire pebffvat bire gur cbvagf jurer gurl vagrefrpg, fb rnpu fcnpr vf nyjnlf npprffvoyr ivn gur fcnprf yrsg naq evtug bs vg, ohg gur fcnpr nobir be orybj vg vf bayl npprffvoyr vs gurer vf n ubevmbagny tevq yvar orgjrra gur gjb fcnprf.
Moving Monty:
Bar bs gur qverpgvbany xrlf (hc be qbja) vf qvfnoyrq ng nal tvira zbzrag. Lbh pna bayl zbir va qverpgvbaf gung oevat lbh pyrnayl npebff bar yvar ba gur tevq, fb gur cbvagf bs rnpu gevnathyne fcnpr pnaabg or genirefrq.
Pushing blocks:
Lbh pna chfu oybpxf gb gur yrsg whfg yvxr va n abezny 4-jnl tevq. Chfuvat n oybpx hc be qbja jvyy erfhyg va vg zbivat gb gur evtug naq syvccvat hcfvqr-qbja. Yvxrjvfr, chfuvat n oybpx gb gur evtug jvyy erfhyg va vg syvccvat hcfvqr-qbja naq zbivat hc be qbja nppbeqvatyl fhpu gung vg erznvaf ba gur gevnathyne tevq. Va bgure jbeqf, ubevmbagny chfurf pna bayl or qbar gb gur yrsg, naq "qvntbany" chfurf pna bayl or qbar gb gur evtug.
Basic mechanics shared by most games in the Covemount series (only read if you haven't played a Covemount game before):
Lbh jva ol zbivat gur punenpgre gb gur synt juvyr nyy gur fcbgf znexrq jvgu na K unir na bowrpg ba gurz. Oevpxf cerirag nyy zbirzrag. Cynva obkrf pna or zbirq va nal ahzore ng bapr. Qbhoyr-yvarq obkrf pna bayl or zbirq vs gurl ner svefg va gur frdhrapr bs fdhnerf naq bgurejvfr cerirag zbirzrag. Oyhr fdhnerf pbagvahr zbivat nf vs gurl ner orvat pbafgnagyl chfurq hagvy gurl uvg n fgbccvat cbvag. Jngre yrnqf gb lbhe qrzvfr. Cerff m gb haqb, e gb erfgneg, naq pgey + d gb fxvc n yriry.
TLDR:
Zbirzrag pna bayl or qbar npebff tevq yvarf. Obkrf zbir fgenvtug gb gur yrsg vs chfurq yrsg naq qvntbanyyl gb gur evtug vs chfurq hc, qbja, be evtug.