1. 一緒に話しましょう would probably be better. Side note, で is not the right particle to use there – should be either に or と, which have slightly different meanings. に implies one-way interation (“talk to you”) while と implies reciprocal (“talk with you”). Are these fill-in-the-blank questions? Because if so, the thing that needs to go before the で is a location – for example, 私たちは図書館で話しましょう = let’s talk in the library.

2.0. Think I’d go with わかりました rather than 理解できました. Otherwise it looks ok.

2.1. “I’m often mistaken about (your?) conjugation of temporal verbs, but I’d like to speak with you.” … Those two clauses don’t really seem to go together. And the use of “you” there is downright odd. Again, で in the second clause needs a location. Or a means – you could say 日本語で話したい = I want to talk in Japanese.

3. Not quite sure what you’re getting at with あなたので – “because it’s you”? The second half reads “I wrote using only small words” (though there’s an extraneous た lurking in there).

4. Technically yes, but it’s more normally just said as よい週末を – the verb is implied.

Side note, the use of the second-person pronoun is not nearly as common in Japanese as it is in English. Or… French?