You'll get lots of help here in forum and others will contribute additional but here's my answers.
1- yes, lower cabinet containing woofer is sealed separately from the tweeter that remains open. Yes, two small holes to pass the two wires from crossover inside the sealed portion of cabinet to the tweeter above. Those holes are best placed just below and behind where the tweeter is mounted. It will feel pretty intuitive as soon as you dry fit the cabinet pieces together to visualize fit and procedure.
2-yes, paint on the outside will seal the exposed mdf from absorbing moisture from the atmosphere. Unsealed inside will allow those surfaces to absorb moisture from atmosphere. This is normal and wood always seeks equilibrium and tries to match its moisture content to its environment, dry or moist. If you live in a high moisture environment such as coastal air, or high humidity than this will have greater affect than in a milder non-humid climate.
Others may disagree with me and say that sealing inside is absolutely necessary, which is fine, and personally I like to always put in the extra effort. However reality is that most retail speakers are unsealed or inadequately sealed and they hold up just fine. Unless you live in a high moisture or highly fluctuating environment, it may not be as critical as you think, but again no harm in the effort. My point is only that this should not be a point of stress. Just do the best you can. Your speakers aren't going to start crumbling or deteriorating if you haven't sealed them inside. They will perform similar to every other unbalanced or unsealed wood surface in your house (dressers, cabinets, bookshelves, tables, etc)
3- yes, if you ever wish to fully remove your crossovers from the cabinet, you will need to either desolder a few connections or install them with enough internal wire slack to pull the crossover out through the woofer opening and place it in front of the cabinet. That means longer wire to tube connectors and to tweeter. Desolder options are disconnecting at crossover or at the driver end. For the input connections I probably wouldn't desolder the tube connectors as they are a little more difficult of a connection, I would instead desolder the wire connection at the crossover. For driver connections I'd desolder at the driver terminals. Yes, screwing the boards to base will be easier to remove than glue, as long as you can reach the screws.
4- no, you probably don't want to build your cabinet with a screwed in only base, or removable panel. The driver opening is plenty large for you to remove and insert the crossover board through the driver opening. Front baffle is 8.5" wide externally, 7" wide internally, minus the thickness of norez on both internal side walls and your probably in the ballpark of 5.25" max width of crossover board and a 5.75" opening for the woofer. No need for any special trap door.
Good luck with your project and enjoy your new speakers.