Motivation. Given the same level of talent and assume everything else equal, the more motivated person wins over the long term against the least motivated person. The former could get more work done with the same mental strength in the same amount of time. The latter has a lower mental strength to productivity conversion rate because of the lack of motivation. So what kind of work gives you energy (e.g. you want to wake up and start working as early as you are physically capable, you keep thinking about the problem even when you take a shower)? If you can't identify what motivates you that's totally normal in your early career. This kind of self-awareness is something you should grow over time.
My default is no but it depends on how much trust I have in my manager. Ask yourself this question "does this person have my best interest in their mind even when it hurts their interest?".
First I would figure out why you would like to switch teams and what you are missing from your current role/team to lead you down this path. A couple common reasons are: work isn't as interesting as you were expecting, career growth stalling, unsupportive manager, etc.
Once you have an idea of your reason(s), you can start looking for teams that mitigate those issues and fit your needs best.
I'll modify your second question a bit by saying "when do you tell your manager?" At the end of the day, you'll have to tell them at one point or another. You need to figure out for yourself if it's worth bringing it up early or not.
Couple reasons to bring it up early:
You can't really go wrong by not bring it up as long as you are ok with not knowing if the above reasons would've been a better opportunity or not. Staying with your current team has advantages as well, you don't have to build a report with the team, your manager already knows you and probably has a pretty good sense of what you are lacking to grow in your career.
Hope this helps!
What To Look For In A Team
First, I recommend going through the following 2 Q&A here:
Something else to consider as you're an E3 is your progress towards promotion and the up-or-out timeline. If you've made a good amount of progress towards promo (9+ months) and you're neutral to positive on your current team, you should consider just finishing that up before switching. For E3s/E4s, there will be a substantial productivity loss when joining a new team, which can easily slow down your promotion or make it harder as you now need to play catch-up.
The beautiful thing about Meta in particular is the staggering wealth of knowledge you have access to when switching teams. This is what you can do when considering a team:
Telling Your Manager