An executrix may be paid for her services. The pay must be based on the nature and complexity of the work to be performed, and the time must be documented. If the pay is excessive, an unhappy heir can file a motion requesting the court review the bill and order the executrix to return any excess pay.
All court-appointed fiduciaries, like executors, are bonded. A bond is insurance or a pledge that the fiduciary will fulfill the duties he accepts and won't run off with the money. A bond without sureties means that one's word is one's bond. A bond with sureties means that there is some sort of insurance from a third party behind that word. A bond with corporate sureties means that there's an actual insurance policy. A bond with personal sureties means that two people have each pledged to put up their money in the event the fiduciary abuses his trust.
Yes, if you can document the time you spent. A good idea is to keep a journal with the date and amount of time you spent on any activity that can be associated or attributed to work for the estate. You should also be able to describe in a sentence or so what it is you did. The same thing goes for expenses you incur while performing these services. Keep all receipts and be prepared to justify what you spent.
Without bond means you serve without having any fidelity insurance. The benefit is that you do not have this additional expense - the bond premium - to pay when you serve without a bond. It is also indicative of the testator's faith in your capacity to effectuate the terms and provisions of their will without the necessity of a bond.
I won't go into a lengthy explanation of the types of bonds as they have been thoroughly explained by the lawyer who initially answered this question.