Transfer Lufthansa to United in Frankfurt

You have not explained in what manner you bought the tickets. I have frequently bought tickets through the United website that involve a local flight in Europe on Lufthansa. That is a single ticket, where I check the bags all the way through, from JFK or EWR in the US. I don't touch the bags again until the final destination. Sometimes that means there is no customs line to go through at the final airport. I do have to do immigration at the first airport (Frankfurt in the case of your OP.) But I don't touch the checked bag.

All distances in Frankfurt are large. But if the tickets were bought together, or even if they weren't, you should be able to make this change.

Since there is always a free bag on international flights, I never try to get away with a carry-on alone. So I can't answer your #1.

When we last flew Lufthansa in 2014, the carryon limit was 8 kilos which is about 17.6 pounds, not 16. Yes the gate agents checked a lot, but not all bags for weight. Seemed like they picked on all the wheeled bags. But its always a gamble, on every airline. But as suggested, we always check a bag on return home, usually full of dirty clothes and expendable stuff. No reason to burden yourself.

Lufthansa will check the bag all the way from Venice to your final destination.
I agree with the above you should check the bag of dirty clothes take out what you need and not worry about it.
It will be easier to make your connection without dragging the bag around.
They sold you the ticket so 1:30 should be enough to make the connection otherwise they will just put you on another flight if they goof up.

We have used the RS convertible backpacks since 2010. We walk up to the Lufthansa gate with these on our back and have never been asked to weigh them, that includes Philadelphia, Newark, Frankfurt many times, Munich, Copenhagen, Budapest. We have checked weight via our bathroom scale at home, and are generally up to about 18 pounds. We've never been gate-weighed on any other airline either, and that includes EasyJet and Ryanair. I fully believe that seeing someone, especially a senior citizens couple like us, carrying softpacks on their backs they are going to assume these are not weight issues. Even if stopped, we could easily decant the iPad and mini laptop into the approved daypack that we have already rolled up inside the bags for the acceptable additional cabin bag.

Both flights should be in Terminal 1. When you arrive from Venice, you will need to go to immigration as this is where you leave Schengen, and a quick additional check for reentry to the US. It is well signed. 90 minutes is enough, they are very efficient, and if your first flight has been delayed they will help get you through, they do not want to have to pay to overnight you somewhere. Be aware your total walking distance could reach 3/4 of a mile depending on where the two gates involved are. if you are lucky your incoming flight will not gate but put you on a bus on the tarmac, this is fortunate because the bus unloads at the center of the complex near where you need to go and shortens your walking. So if you feel you need a snack, wait until you have gone through all clearances and are on your way to the gate so you know if you have excess time. Boarding for a large transatlantic plane will likely start 45 minutes before your scheduled departure. We once made a connection there entering the terminal 9 minutes before departure; we made the gate one minute prior, I believe they held for us.