Hello. You have two issues there: 1. the automatic redirection to HTTPS and 2. the unsafe content that makes browser show your site as insecure.
For (1) the fix depends on the server you use. I can help you with this if you use an Apache Server.
For (2), like you say, we have to hunt every occurrence of every external resource (images, javascript, etc.) and switch them to load over HTTPS. Possible problem here: that for some of your external content there's no HTTPS version available. We'll have to see what options we have if we found that problem, cannot state a solution before hand.
As you said the fixes are simple, however do not confuse "simple" with "no work required": piling up chairs is easy, but is not the same to pile up 10 chairs than 1000.
My current bid covers the fix for the HTTPS redirection provided you have an Apache server and that you have shell access for root to the host. (We can work out a solution with an .htaccess file if you don't, but the best path would be to configure that on the virtual host directly. And also covers a normal amount of changes, let's say 10-20. But if there are more than that, I'd need to re-evaluate the task and maybe add another milestone.
I hope we can work together.
Regards.