Using only trains that don't need a reservation is OK. In 99% of the trains you'll find a free seat,. Especially if you're alone, you can often find a free seat.

If however a train has mandatory reservations, it is a bad idea to board it without having one. You'd better go to the ticket office and ask for one. You could bee fined, get thrown off the train, or made to pay an on-board fee, which could be triple thee normal reservation costs.

Would the interrailing planner app tell me if a reservation is mandatory?

Yes it would. Although it is not without errors, it is mostly correct.

For Italy, the best is to use the Trenitalia website. It is more complete and up to date than the rail planner app. For reservation-free options, click on the dropdown that says "main solutions” and select "Regional”.

Also the most wide covering site of bahn.de (German rails) has fine details and tells exact if a train must be reserved or not. IF you want the NO REServ/fast train option, then click on ´nur nahverkehr,, but this works fine for DE and not always good for other countries.

BTW- Your planned trip to Paris-the French sectors, must take much more time this way and also force you many more changes. Same for In Italy.

IF you travel on/around long weekends (coming up 26-30/5 and the weekend after 4+5/6, christian holidays, then expect big crowds and it may be after all be  a very wise idea to spend the odd€ to REServe that seat. Last Easter (I am currently on a Inter-trip, now in Praha, before Austria) there were many tales of overcrowded trains that had to stop and cleared by railway police.

Thank you. Would this be included as a travel day in the pass? 

If I reserved a seat would this be included as a travel day in my pass (as well as having to pay for it) or would I then have an extra travel day. Also could I reserve seats when I’m in the country or is that too late? 

As long as it's with trains of the participating companies, you can use them with your pass (and as many trains as you like on a travel day). In Italy, that's Trenitalia, Trenord, Micotra. There are other operators but you're not likely to encounter them if you're travelling between the big cities and/or along the main lines.