Frankfurt-Munich-Baden Baden -Zurich-Assisi-Rome in 5 weeks

There are others here more expert on European rail fares than I, but I suspect that a multi-country rail pass may not pay off for you. Germany has some good deals on trips within its individual regions, and Italian rail fares are pretty inexpensive in general. If you are able to pin down the date and time of your longest German and Italian travel legs (including the one from the Swiss border to Assisi), you can save a lot of money by buying low-cost (but non-refundable, non-changeable) promo tickets.

Switzerland is a big question. Its rail fares (like everything else in the country) are very expensive, and several different transpprtation passes are available. But your former exchange student's family may offer to drive you around on some days. I suggest asking their advice on what places they recommend that you visit and what rail pass, if any, you might benefit from. If you want to go way up to mountain peaks, that can be quite costly.

I wouldn't consider myself a railroad expert, but I would agree that any kind of expensive Euro pass doesn't seem to make much sense on that tour.

For Switzerland, I assume that your friend will be taking you around, so you may not even be doing much train traveling there at all. From Assisi to Rome, you will be walking. The Maltesan railroad system has disappeared completely since 1931, so you would have to find out if that pass would be valid at all on their bus system.

So basically, you will be going straight from A to B with most of your train connections. That leaves only one week of Germany and that one week of vague "travel" where you may be traveling more frequently and more spontaneously.

Sounds to me like it will probably be much less expensive for you if you try to find some other special offers instead of that pass.