Eclipse: Second Dawn for the Galaxy

Yes — ships can pass through sectors with enemy ships only if they are not pinned; during each Move Activation each opponent ship in a sector pins one of your ships (of your choice), and pinned ships cannot move from a sector containing opponent ships (see p.13).

To Retreat, move your ships to the edge of a neighboring sector that has a Wormhole Connection and that contains one of your Influence/controlled ships (players with Wormhole Generator have expanded options); retreating ships cannot Attack or be Attacked once they complete their retreat on their next Ship Activation, but they remain eligible to be targeted until they’ve actually moved (see p.19).

You pay during the Upkeep Phase after activating Colony Ships and collecting Income; if you cannot pay you must Trade or Abandon Sectors until you can pay, and if you still cannot pay you are eliminated from the game (see p.24).

Each tech you have in a category gives a discount on further techs in that category, but every tech has a printed minimum Science cost that discounts cannot reduce below, so a tech cannot be made cheaper than its minimum (see p.10).

When Exploring you may place a discovered sector and immediately take its Discovery Tile only if the sector is undefended (no Ancients); Discovery Tiles from sectors containing Ancients are only awarded during the Combat Phase, and when you take a tile during Explore you must reveal it and choose its side before the activation ends (see p.9); during Combat Phase unresolved Discovery Tiles in sectors with your ships are claimed as part of the Combat cleanup (see p.21).

Control changes are handled during the Combat Phase cleanup: after battles are resolved you may remove the controlling player's Influence disc and place it on their Influence Track, then move Influence discs from your Influence Track to any sector where you have a ship and no disc; resource/production effects happen during the Upkeep/Production steps later (see pp.18 and 21).