LinkedIn is one of the most protected websites out there so you always risk getting the account banned. But at small scale, it should be fine. Crawlee has support for Playwright + Firefox with statistically generated fingerprints (you can also pass your own fingerprint) which looks pretty human-like. Put some random sleeps in between actions so it looks like you are actually using your mouse.

To send emails, you can use any 3rd party tools, check out Apify as Crawlee is well integrated there and they have email sender easy to use.