1) Well it depends on what the property is. State Farm has insured one of my SFH properties that I own in an LLC, but if it's 5 units or bigger and considered commercial, then you're going to have to find a commercial broker. Since an LLC is considered a legal entity, there should be no reason you should have any trouble finding insurance. Perhaps contacting your current policy holder and take out a new policy under the LLC and cancel the current one.
2) Is it every Easy? haha Once you turn over the property to an LLC, all loans, in my experience, will be in the commercial realm assuming your looking to do a basic HELOC and not some crazy collateral based loan.
We own all our properties in LLCs, not as crazy as every one in it's own LLC (too much paperwork and accounting) but everything is under the LLCs. We have no problem with financing, although we have only done' cash out refi and not HELOCs.