Also not a tax/legal professional, but agree with durhamlad. On each point:
Can I give the money to my husband (UK citizen only, never lived in USA & have filed 'married filing separately') and he can reinvest it? There is about £25,000 I guess.
This would not be taxable. There is a limit on gifts to non-US spouses (have to look it up, but by memory it's something like $120k a year) - if you exceed that limit, you would need to file a gift tax form on your US taxes, and the gift would be deducted from your $11 million-ish lifetime limit on gifts and estate taxes. Unless you expect your estate to exceed that $11M-ish limit, gifts are not much concern (if you find yourself in that lucky situation, some professional estate planning advice would be a good investment!)
There are options for US citizens investing from the UK, but none of them are without complications. See the list here:
https://www.bogleheads.org/wiki/Investing_from_the_UK_for_US_citizens_and_US_permanent_residents#Investment_account_options (disclaimer: I wrote a large part of that page, although other contributors have reviewed what I wrote - definitely not professional advice). Happy to answer any questions on those options if I can.
Next thing, my father passed away recently and I am due some inheritance money. Is this taxable? ... If this is the case,
should I have it all paid straight to my husband so it never reaches my bank account?
Receiving money from an estate is not taxable in the US or UK. No harm in it being paid into your bank account (US or UK). If it passes through a non-US account with your name on it (including jointly), you'd report on FBAR and form 8938, if you exceed the applicable limits.
We are thinking we may put it towards buying a second property to either flip or rent (which I guess is taxable) and that it would be better to have the second property in his name only so there is no obligation to add any of this to my US tax return.
Capital gains from a non-primary residence would be taxable in both the US and UK, as would rental income. Foreign tax credits apply, so you probably wouldn't actually owe any US tax if it was partially in your name, but you would need to report it to the US. Putting the second property entirely in your husband's name would mean it all gets reported on his UK tax return, doesn't touch your UK or US tax returns. Depending on the income level of you and your husband, that could result in higher or lower taxes (e.g. if he's a 40% payer and you're a 20% payer, choosing to have him have 100% ownership of the house would result in paying higher UK taxes). Having the non-US spouse have assets entirely in their name isn't an uncommon strategy. Consequences in case of divorce or unexpected death (and thus impact on estate taxes) should be considered.
After this streamlined procedure, the stress, the cost, the ongoing obligations to file every year, I'm now seriously considering giving up my citizenship. We don't earn much money at all and this has been a huge cost to us as a family. I have always been good at saving and investing, most of which went towards buying our house but now feel like I can't even do this as the cost to fill out the forms is so horrendous (more than i'd even make in gains for a year).
Renouncing US citizenship is an unfortunate but common step for US citizens living abroad, especially people like you without any significant ties to the US. There are more hoops to jump through and more costs to pay, but when its done you'll have no US tax complications ever again. It's a very personal decision, so I won't make any recommendation either way, but certainly an option to consider.