After I re-install outlook with the todoist plug in in my new laptop will all my created tasks be there?
All tasks are stored in the cloud so as long as you log into the same Todoist account, you can reinstall all our apps and plugins and the synced data will be loaded from the server as you log in.
However, please note that if you reinstall Outlook and will have no emails in Outlook after that, then the task you've created as links to email messages will not work as these messages won't be found.
If I create a email task using the chrome plugin, will this task link to my email in the outlook with the Google sync and the other way around?
In this situation - most likely not. The Chrome plugin uses a completely different link format - it saves the URL pointing to the message in Gmail, while the Outlook plugin needs and uses a custom local link to the message in Outlook so combining Outlook links with Gmail links won't work.
If that's what you've meant in the message I just replied to a moment ago then unfortunately it won't work due to the link format differences.