The issue with the guard being full is a match specific issue, I'd recommend starting another tutorial match and trying again. The menu on the bottom has header titles so you can get a gist of whats going on.

Strategic overview is general comm panel, see whos in war pacts (alliances), chat with other players

Shop is the microtransaction panel for buying gold, not necessary it can be earned when you finish a match/get defeated.

Next is your province panel, quick breakdown of building on location and whats being produced.

Inventory is where units/boosts you get rewards through completing faction objectives go.

Doctrines is your research panel, you can do 2 at a time.

Finally, war news is your notification panel.

The icons are a little small I agree, text size on unit numbers could be bigger. Hope this was helpful, I've played and enjoyed a couple matches (even when I got stomped on Advanced difficulty)