Depends on what you want to see/ do. Even 10 days in Tokyo won't be enough for me

Don't have to make it so complicated. Just either buy a SIM card, or use roaming with your telco. It's the same case when you visit neighboring countries like Thailand or Singapore.

If you're talking about cost - check out few SIM prices. As rickarch mentioned you can try Hello1010 sim card. I've always used Hello1010 and there's no issue except for my last trip to japan. I couldn't activate the SIM; so i had to ask my friend to activate it via her phone before I could use.

One last option is you can purchase SIM card in Japan itself.
Refer to the above, and Page 1 Post #1 information.

Yes of course you can lug your baggage around the train stations but as you mentioned - peak hours - will be hellish especially main stations like Akihabara, Shinjuku, Shibuya etc. I arrived in Shinjuku station at 8pm and it was really high traffic. You'll need to know where you're going. If you're blur and unsure of entrance/ exit, make sure you're standing at one side/ away from the incoming/ outgoing crowd. Don't block others' road by standing in the middle (it may happen unconsciously when we're too focused on finding the way).
If you want to avoid crowd, just make sure you don't visit coinciding with the games' period. Eg. game starts 20th Sept so you can visit Japan early Sept, or after the games - 2nd week or mid Nov. Then again, it's not Olympics so probably the impact of crowd would not be overwhelming. Maybe those staying/ stayed in Japan can shed some light.

I bought from klook. RM50+ for 8 days 3GB. I'd say super cheap cause my brother in law bought for around RM300 for Docomo unlimited data SIM while I just go and pick the klook SIM from another counter. However the speed was a bummer as I think the data has ran out. Better to buy the unlimited 8 days for RM80+. Or just get a samurai pocket wifi pick up from KLIA, super fast speed.

You can bring your luggage on JR trains no problem, even on yamanote green line at peak hours, but if you're in group of more than 2 expect to be split into different doors or even trains I even carried baby stroller but the stroller had to be kept