Some of this is difficult to answer because I have never been at a firm which didn't e-file... my first tax season was 2005 so I don't have the greatest comparison to what you're facing.
1 - I prefer to meet the client after the return is prepared**. The post-prep meeting allows me to review the 2 year comparisons with the client, showing why their refund/balance due is higher or lower than the prior year, etc. They'd sign the 8879 and pay at the meeting. In these COVID times I upload a draft to the client portal and have a phone call if the client prefers that or the numbers are way off from last year, or good old snail mail for the clients that shouldn't be allowed near a computer.
I have some remote clients, where I use eSignature to get signatures. It's an extra step and a learning curve, but once a client has gone through the process once, they love it the second year.
2 - Most of the time, yes, but I make exceptions for business clients and people I know are good for it. You can create your own rules however you want, and many firms require payment before e-filing 1040s. Client gives you 8879 with payment, all one step.
3 - No. Actually, I charge extra for a paper-filed return... assembling... stapling... slip sheets... UGH! Death by a thousand paper cuts!
4 - I can't speak for Lacerte but I'm sure it's fine. The main thing to do is have one person in your office in charge of all e-filing.
I don't believe that my AR is higher than it would have been before e-filing but that's really tough to judge. As far as merchant fees, I do accept card payments through Square and have since I started my own firm in 2015. It's a convenience for some clients, making it easier for them to use my service, but for my remote clients it's a godsend. Sure, it costs me about 3% of the fees for those that use it, but not every client uses it. And a client that moves away that I can retain pays for 20 others to use their credit cards.
** Getting your firm to the point where you could do this is probably out of scope, but I do want to mention this as it is part of my process. With easy clients (pre COVID) I prepare the return while they wait. It fits in with people's busy lives, and we turn a stressful occasion to a more enjoyable meeting. The client brings the documents, I prepare the return, we review the 2 year comparisons, they sign, they pay right away. While their return is being printed, I scan the documents and assemble everything. No AR, no WIP, just in and out. On these, I do hold e-filing for at least a day in case of the dreaded "I just remembered X" phone call, but normally we identify missing information during the prep meeting. There is a variant of that where you prepare the return while the client is there, review the draft with the client, but not finish it that day.