It would very much depend on context to pick the exact verb needed.
- il offre du fin en cadeau: he offers wine as a present
- le serveur suggère du vin rouge avec le plat principal: the waiter suggests red wine with the main dish.
- en apéritif, puis-je vous proposer du vin ?: as an aperitif, may I propose wine?
With simple tenses, no, they don't change: il propose, elle propose
With compound tenses, they can change in the form of their past participle, mainly with auxiliary "être" which make them act as adjectives:
- il est allé à l'école - elle est allée à l'école. (active)
- le vin est bu par l'homme - la bière est bue par l'homme (passive)
The rules are different with auxiliary "avoir", but you will study that later.
It's not going to be "corrected". The computer program that does these duties is not particularly clever or well-constructed. It has a list of possible correct answers, and one of them is the one it shows as "the" correct answer.
Among the program's other shortcomings is a lack of recognition that French is a language with an enormous number of homophones - i.e., words that sound the same but have different meanings. Prominent among these is the fact that many (but not all) subject/verb combinations sound the same in the singular and the plural.
People have been reporting (and complaining about) this for years, quite justifiably, and I have noticed that some of the exercises have had the "other" singular/plural answers added fairly recently.
Some of the older exercises, when confronted with an answer which is not "the" answer, will show you "another correct answer" if you give it one of the other answers on its list. It should do that when you give a plural answer and it's expecting a singular one. But it doesn't, and I wouldn't hold my breath waiting for it to catch up.