It really depends on the person's accent. If you are from England, the word "party" would sound more like "potty," but in most of the USA, you would pronounce the r, and it would sound like "party." British accents tend do leave out a lot of consonant sounds, specifically the "r" sound, so your English pronunciation really depends on the accent of the person teaching you. I hope this helps!

What you hear will depend on the accent. In some parts of the world, the R sound is sometimes light and in others it is harder and much more noticeable, but it is certainly always there. Understanding of what is being said will also depend on context. Most people don't use the word "potty," in general conversation as it's usually used with children to describe a toilet, however, to be absolutely sure when you are totally lost, you can always ask the speaker and confirm what they mean to say. I wish you luck in your studies!

Regional accents do make a difference, but in the US, I rarely hear anyone's accent so heavy that I can't tell the difference. I only remember one instance with a guy from Maine.

As already stated above, it really depends on the country. England and Australia perhaps omit the "r" sound, but countries like Canada and The USA usually pronounce the "r" sound. Good luck!

"Is pronounce" in your question is not a correct verb tense. You should review the three forms of the present tense so you know how to construct a question correctly.