Welcome to the community!
I’ll second the post by Hans, definitely read the ToS, before you even do your first job, or your career here could be over before it even started.
Sharing contact info unless absolutely needed for the service you provide
(e.g. if you provide business card design, obviously you need the client’s email for the card, but they don’t need yours)
is a big no, and even then it needs to be on the order page of an existing order and not in the inbox “chat”, at least that’s what support usually seems to say.
You might get messages that are harmless spam, or phishing attempts (such that ask for your email or ask to click on some suspicious link for more info might be), people who’ll openly or secretively ask you to break some of Fiverr’s ToS, like people wanting to make deals outside of Fiverr, or want you to do a job for them that isn’t permitted on Fiverr (the infamous “create an account on (other platform) on me” , etc.
You really need to read the ToS thoroughly if you don’t want to risk a warning or even immediate ban, some terms are intuitive, some not so much, so, really, read them, and read them well.
I also recommend reading the articles Fiverr provides both in the Seller and the Buyer Help Center (link on main page under Help), they help a lot to understand how everything works and to be well-prepared for any situation or pitfall that might occur.
Last but not least, this forum is a treasure trove of info, including and beyond the help and info material by Fiverr itself - just keep in mind that forum means peers, and personal interpretations and opinions often not necessarily are “official facts” in many cases.
There are a lot of knowledgeable people here but occasionally you can find “great tips” that could get you into trouble.
Use common sense, don’t just read "tip topic"s opening posts but skim the comments (often if there are iffy things, others will chime in to caution) and if in doubt, get at least a second opinion.