You need to add accessory exercises, as many of them as you can, focusing of firing the lower back muscles. Obviously.
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No, wait, maybe I wasn't very clear. I'm not squatting and deadlifting every day, there is one day in the programme when you're supposed to do both. That day kills me because I get tired in the lower back from the squat and I can't deadlift heavy (heavy relative to my strength).
In reading the helpful column below, I think it's unlikely that your relatively light squat is hurting your deadlift significantly. Have you tried a reset in the deadlift? I would try that, drink more milk (I drink skim because I'm fat) and film yourself to evaluate your deadlift form.
Artificially Weak Deadlifts, Part 1: Perception vs Reality | Robert Santana
Going back to the original questions:
No, yes, probably not.
Remember, both the low bar squat and the deadlift stress the posterior chain. You started with a deadlift that was quite a bit higher than what someone who came into the program totally green. As a result, your back is starting to feel a lot of stress that it's not adapted to. My suggestion for the deadlift would be to work up to a weight that you can do for a set of 5 without a form breakdown (as described in the book) and then continue adding 5 lbs per workout from that weight. Your back will adapt and the squat and deadlift should become mutually beneficial to each other's progress.
A belt will help you continue to add weight to the bar, as you learn to use it, but it's not going to make your lumbars work any less.
Might be that your lifts are not being performed correctly. I know I wasn't, so I got coaching by Robert Santana in Phoenix. My deadlift was trash and I always felt it in the low back. By the end of the Intro to Barbell session, Robert fixed this for me and I could feel my entire back performing the exercise instead of the low back. Really felt my whole back the next day after not doing it correctly for so long. If you have a Starting Strength coach anywhere in your state, find them, or maybe consider keeping an eye out for a camp in your area.
Get yourself some coaching. If you feel that your lower back is sore after deadlifting, your form is dogshit. You’re probably unable to hold your back in extension and/or you initiate the pull with the hips rising instead of pushing through the floor. As for squatting and deadlifting on the same day, in the long your recovery will be better, since you’ll get more rest in between sessions.
I would not agree, again I said the "most simple" adjustment. That would be going to Deadlifting 2 days per week, and if you are working in Cleans on B days it would end up being first week 2 deadlift sessions and week 2 would only have 1 session. If not doing cleans then just deadlifting Day 1 and Day 3, as that gets to be too stressful then just Deadlifting on Day 3.
Eventually if you train consistently for a good amount of time a 4 day split is a good idea, deadlifting once every other week while using rack pulls, deficit deads, halting deads or some other accessory movements on the in between weeks. This is all assuming that form is acceptable and you are recovering properly by eating and sleeping as you should be.