It does make it feel a little smaller but that's easily solved by adding a box around the active sector area to demarcate the boundary. Putting things like gas clouds and asteroid belts in the corner regions helps too and a large number of the sectors I saw while playing happened to have things like that which is probably why it didn't stick out to me much.
And trust me, if I feel that strongly about something you'll hear about it lol. I think it lends to a certain "feel" when it comes to the general UI and the key with that is to keep things as consistent as practically possible like making the jump zones swept. The round sector area works nicely with the detection circles specifically because they're both round. In order to really pull that off on the grid design you'd have to look at how bold and vibrant the grid lines are relative to the detection circles so that the visual contrast between round and square is negligible. It probably isn't difficult to adjust but finding that balance between light enough to see and use but faded enough to not disrupt general viewing could be tedious. Then again you could bypass that entirely if you wanted by making a slider in the options menu which would allow each individual player to adjusts line opacity. Just some thoughts off the top of my head.
Yeah, the context menu for stations is a little trickier now. I think it's supposed to pop up after you've hovered over the station or ship for a brief period but I've found that it's easiest to have your own ship selected, left click on the AI asset (be it a ship or station) then hover the mouse until the menu pops up.
Currently ships auto-repair if I'm not mistaken. I seem to recall a "repair beam" type turret being available but you've either have to spawn with it or find it in a trade hub/station. I'd expect that AI and, eventually, player owned stations will be able to repair ships also down the line. I just don't think that's in yet.