1) It's likely you would still owe nothing, but there's no guarantee depending on various scenarios. On strictly earned income where UK tax is withheld, it's probable you would still owe nothing, but UK tax free allowances enter the picture. If (UK) earned income is in the area of $10,000 to $20,000 a year with UK personal allowances resulting in £0 or a small amount of UK tax paid, FEIE will probably give a more satisfactory result. If the UK income is in the area of $50,000 and above, FTC (1116) will likely give a satisfactory result.
There are no hard rules, one must run the figures both ways to be sure, but if using FTC, the 5 year rule on switching back to FEIE does apply.
2) NO, POSSIBLY, MAYBE, PERHAPS.
Be sure you understand the "baskets" associated with FTC, and the rules applying to carry forward/carry back. Passive FTC's can not be used to offset General Limitation (earned) income nor Resourced income, and vice versus.
FEIE is generally seen as an easier method for those on lower incomes. When incomes are greater, FEIE can become more complicated and FTC usually gives a superior result when the income is from a country with higher tax brackets (like the UK).
EDIT TO ADD:
Using the FTC method opens up investment opportunities in the US (IRA, ROTH) which are unavailable when using FEIE. Perhaps someone better qualified to speak of these will respond.