My car was hit yesterday and (likely) totaled. I need a car for work and have never been in an accident. How do I handle this, is there a guide to auto insurance? (CT, USA)

EDIT: UPDATE AS OF NOV. 16, 2022

Geico is giving us the run-around. As some redditors have noted, Geico is experiencing severe labor shortages as they have been closing offices, making layoffs, and facing resignations. See /r/Geico for the drama. I am almost definitely changing insurers after this.

Anywho, we contacted Geico who had assigned a "Liability Adjuster" and an "Auto Damage Adjuster" assigned to the claim. We were told that the other driver (who caused the accident) has only the state minimum coverage for property damage liability, and if he is determined to be at fault by Geico, he will be on the hook for the below list.

What's incredibly frustrating is, we contacted the Auto Damage Adjuster who is supposed to be in our local area and complete the inspection of my car at the local body shop. He told us that his supervisor assigned him to go work in another state for this entire week, and given the Thanksgiving Holiday, he may not be able to inspect my car for weeks. This will result in $75/day storage fees at the body shop for a delay out of my control. As an aside, does anyone know if there are laws or if I have a right to a speedy inspection?! Wasting 2+ weeks from the date of the accident seems insane to me.

Anyways, the other driver's policy is likely going to have to pay for:

1. damage to my car
2. damage to the BMW he pushed my car into
3. damage to the utility pole he pushed my car into
4. storage costs for my car at the repair shop, and
5. reimbursement costs for any car rental I make.

I am kind of of the opinion that, given this guy has a limited amount of coverage, I should do my best to minimize #4 and #5 above. I don't want to rent a car only to find out I won't be reimbursed. Similarly, I might have to get my car towed to my house, rather than sit at the shop and incur $75/day storage fees which eat away at the funds available.

I am very concerned that Geico is on either end of this (my insurer and the other driver's). I worry that they will try to assign part of the liability/fault to me, though I did absolutely nothing wrong. If that happens, I may get an attorney and/or file with the State of CT's consumer agency that deals with CUIPA (Connecticut Unfair Insurance Practices Act).

All of that being said, I don't feel like getting a lawyer will be worth it. My car is only worth maybe $8k, I was not injured so no medical bills. I am actually a lawyer myself but work in a completely different area, so I don't know much about insurance law.

ORIGINAL POST IS AS FOLLOWS:

I am in Connecticut, USA and yesterday I was hit by a driver who failed to look before merging. I have (had?) a fully-owned 2010 Subaru Forester.

I have never been in an accident before so I wasn't sure how to proceed; is there a guide for this sort of thing someone can link me to?

Details of the accident:

Another driver (insured with Geico in CT) merged into me, sending me off the road into a telephone pole. I suspect my car will be totaled, because the airbags deployed and the front end is totally smashed, radiator leaked out, etc. I called the police and made sure they made a report (to be published soon??), and the other driver stated it was his fault to the LEO.

Steps I've taken thus far:

Once the police OK'd it, I called my AAA coverage and had them tow the car. AAA actually arrived early while the police were wrapping up, the AAA employee recommended that I call around to various auto body shops to confirm who had space. I did so and identified a local body shop, where I had my car towed to.

What do I do next?

I desperately need a car to get to and from work, however I do not have rental reimbursement on my own auto policy. I have Geico as well. I have collision coverage with a $500 deductible. My questions are as follows:

1. I am under the impression that I should not make a claim under my own policy, because the accident was not my fault—is that correct? The insurance agent I spoke to told me I could "use my deductible" on my own policy to get paid out faster, but isn't that counter-intuitive given I did nothing wrong? Wouldn't that result in me eating the deductible, or would I be able to be reimbursed for that?
2. I contacted Geico and stated I would like to make a claim against the other driver's policy. They stated they had assigned an adjuster, provided me his phone number, and said they would perform an inspection "soon" at the shop I had my car towed to—am I correct in guessing this will take weeks? Should I have the car towed to my driveway to avoid storage fees?
3. What kinds of questions should I be asking the insurance adjuster?
4. How can I get a rental ASAP? How long should I expect to get a rental for? A bit of googling indicates that I should be permitted to get a rental paid for by the other driver's policy once "fault" is determined; from what the adjuster told me over the phone, it seems the other driver basically admitted it was his fault, and Geico won't need to wait for the police report to make a determination of fault. It sounds to me like I should be demanding a rental now, right?
5. Do you have any advice on how I should proceed?
6. For future reference, where should one tow their car after an accident? I didn't think to have it sent to my house, but maybe that was the right move?

I already understand the haggling process once Geico is ready to write me a check for the car's value; it's getting there that has me confused.

Thank you so much, I am so frazzled.