Memoir '44

Yes — but it depends on unit type: standard infantry may move 1 hex and attack or move 2 hexes and not attack; elite infantry may move up to 2 hexes and attack; armor may move up to 3 hexes and attack; artillery may either move 1 hex or not move and attack. (pages 6–7)

No — a unit adjacent to an enemy is in close combat and must attack the adjacent enemy unit(s); it may not target a more distant unit instead. (page 7)

Yes, many terrain types (and intervening units) can block line of sight for units that require it; however artillery do not require line of sight to attack. (pages 8–9)

When a unit must retreat but cannot (blocked by terrain, units, or the board edge), you must remove one figure from that unit for each retreat move that cannot be completed. (page 10)

Yes — after taking ground in close combat an armor unit may perform one overrun (a second attack) following normal attack rules, with only one overrun allowed per turn. (page 11)

Yes — any dice penalty applied to the attacking unit and the terrain protection of the target are cumulative and reduce the number of attack dice rolled (note that artillery normally ignore terrain protections unless specified otherwise). (pages 8–9)