On Sistanis website it states «If someone keeps a recommended fast, it is not obligatory on him to complete it. In fact, if a fellow believer invites him to eat, it is recommended for him to accept the invitation and to break his fast during the day, even if it is after ẓuhr.»

1- If I was to fast the 13th of a month, with the intention of fasting the 13th, 14th and 15th (in order to have the reward like I had fasted the whole month), and a beliver invited me for dinner, should I accept the invitation and break my fast? If I do that and still fast the 14th and 15th, would that still count as having fasted the whole month as the hadiths states?
2- What if a fellow beliver offers me something to eat, like tea or biscuits, should I still break my fast, and accept the snacks? He doesn’t offer a proper meal or anything like that, just some snacks, is that also something that I should accept and break my fast to eat it?

1- Yes. It will be counted.
2- No. According to S. Sistani, snack is not considered.