I like your work - especially the ANM bag - it is well-researched and a very viable product.
I am missing a design process for the vial tray, and that is one of those projects where you can impress future employers with.
Why is TPE the right material, it seems to isolate the vials from the cool pack, why not a lunch box type design or a kind of pouch/sleeve.
With a disruptive innovation such as Theia, I would like to see you tackle multiple perspectives needed to bring this device to the market - test it with users to see how they will use it, and a small business/marketing plan with a sales&distribution model.
Your exercises are good but you can make a selection of the best work. You obviously have a good sense for design.
If you do a CAD form exercise, it has to be perfectly executed. I like your first design for the TV stand the best.
Your sketches are decent overall though you can work on creating your own style more, being more expressive and while these sketches are quite flat, see if you can make them pop off the paper with a more 3D feel.
I think the first thing I would be looking for in an intern is if his work fits to the company, it is always good to have a clear profile - what kind of projects do you want to do and in what kind of industry/markets do you want to operate. Then it is about what you can specifically mean and the least I would expect from an intern is good ideas, an efficient work process, presentable visualisations and good CAD skills.