Loco2 is good. You can cross check with Eurostar.com and captaintrain.com

No space issue at all. There are some limits, but this is well within them. Note that you carry all baggage on board yourself, and will be expected to put all bags through x-ray machines yourself.

It's an easy transfer on RER line D (kind of an express metro) which is direct between the two stations. You only need a metro ticket for this journey, but do need to use it to open barriers at entry and exit. Only difficulty can be the slightly convoluted nature of the station layouts, but as long as you follow RER D (towards Melun) and then Grandes Lignes or TGV on arrival, you'll be fine.

If you are sold this as a through itinerary, then you are protected by international convention (CIV) in case of missed connections - however, this may not be very convenient, given the limited number of trains from Paris to Milan. In my experience, however, Eurostar is either punctual or disastrous...

If you do have a longer connection time, there are left luggage lockers in the Gare de Lyon, and you could then get to experience the wonderful Train Bleu brasserie. Your also near the Promenade Plantée, the inspiration for New York's High Line.

I've never felt unsafe in central Milan, personally, just use normal precautions and be aware of your surroundings.