Are there any online websites to get Persian exposure or have a discussion with native Persian speakers? (or maybe find people to exchange languages and practice together)
Online Language exchanges work quite well, there are many to choose from, Google ("language exchange websites" knows them all.
On such exchange, you can find people who wants to learn your language (I assume English) and teach you their own. Most are not language teachers, but native speakers. You find a partner, and talk over Skype. You don't pay anything, but you teach your partner your own language in exchange for theirs.
There are other online platforms, like iTalki, where teachers give online lessons, those might be cheap but not free.
Most language exchanges (I looked at) have "freemium" business model: You can create account for free and look around, promote yourself and maybe even accept contacts from others, but you need to upgrade to paid membership to be able initiate the contact with others. Usually you cannot enter (it will be manually deleted) direct contact info into your profile (because website is paid by the upgrades).
Some people still find sneaky way to enter contact info without paying the upgrade, to use it for free, but I do not think it is right: If service provides value, you should pay for it (it is not expensive: just few dollars).
You may want to make research about how many current (recently logged in) members are from the country of your interest, and think about how to make good (inviting) profile. Look at some profiles and see what makes them interesting to you.
Full disclosure: I occasionally pay for upgrade on MyLanguageExchange.com - but have no financial interest in it. Promoting it increases value of my membership (more contacts) but I do not profit from it.
Some resources for getting exposed to Persian:
aparat.com (basically "Iranian youtube")
namasha.com (another -less popular- Iranian video sharing website)
telewebion.com (Live broadcast and archives of Iranian state TV, including Persian/Persian-voice-overed movies)
upera.shop (a website where you can buy and download Iranian movies, also accepts international payments via bitcoin/visa/mastercard)
And here are some of the most popular native Persian speaking internet forums:
forum.persiantools.com (Relatively general-purpose with a mild computer/technology focus)
forum.p30world.com (Relatively general-purpose with a mild computer/technology focus)
lamtakam.com (new startup QA site, with mild Language Learning focus)
talk.zabanshenas.com (English learning forum for Persian speakers , but you won't have problem asking questions about Persian, even in English)
forum.majidonline.com (3D, Multimedia, web programming)
applyabroad.org/forum (Immigration forum, here you can find native Persian speakers who are looking to learn your native language (e.g. English, German, Italian etc), and practice with each other)
discord.gg/hJnGsZT (a general-purpose discord server for Iranians)
discordapp.com/invite/Rqx4NeC (another general-purpose discord server for Iranians)