I'm not sure there are cut-and-dried answers to any of those questions - but here are my general views.
i. Vesting schedules and external investment
On the structure the founders have agreed, the question is - does it make sense? If it does, then let it stand. If it doesn't, and you and they believe that your joining the team is a big step forward, then discuss that frankly.
If there's an external investment, it's inevitable that a whole lot of things change. Usually, I'd say that's beneficial for the early stage team - because it's usually tidier all round to (for instance) bring forward the vesting schedule.
ii. Founders' Equity
If you're critical to the success of the project, I'd say that should be recognised in the class of equity you're offered. So yes, you should ask. And if the answer is 'no,' take professional advice about what the junior class gives and doesn't give you. What's it worth in the compensation package overall?
iii. Taking a %age of funds raised
If the purpose of raising funds is to invest in the project to which you're going to be committed, I'd say 'no.' It's a team challenge, and your value to the team should be picked up in your compensation package.
If the purpose of raising funds includes the founders taking cash out of the business, then it's a qualified 'yes.' If you're making that event possible for them, taking a percentage is a simple way of avoiding some very complicated negotiations!
And if the primary purpose of hiring you is to enable funds to be raised, then again I'd say 'yes.' If they hired you just to raise the money, that's how you'd be remunerated.
iv. Termination clause
One issue you often find here is the 'good leaver/bad leaver' question being tied up with whether vesting gets accelerated, held or cancelled. Again, look at the overall shape - what classes of equity are defined and offered, how it vests and what the thinking is behind that. In case of termination, you are clearly looking to protect your interests. And if it's not clear, take specialist legal advice. I've met too many people who've negotiated what seemed to be good termination terms but have found themselves disadvantaged. When that happens around a success - for instance, a big investment round or an exit - it can be pretty damaging. It's uncomfortable thinking these things through when you're getting excited about the venture, but far better to sort it out up front!