Hi Erik.
I assume you mean SharePoint Online standard edition. Refer to the service description document from Microsoft which you can find here:
http://www.microsoft.com/downloads/details.aspx?FamilyID=1bef6a35-9785-4a0b-b227-387c0ee85a36This will provide in detail the features that SharePoint Online supports.
To briefly summarise; some of the points that you mentioned are not supported in SharePoint Online. Specifically custom code, uploading features, changing the web.config, there is no My Sites etc. Therefore you would certainly need to make some adjustments moving from on-premises to online.
On the topic of custom code, we have found that not having it doesn't necessarilly limit your capabilities to produce compelling solutions that help the business work better.
Hope this helps.
Myles
http://www.thinkscape.com/SharePoint-Online-Consulting/