1. Is Delta timing good for a incremental/click based game?
What is an incremental/click based game? You mean like cookie clicker? If so then yes, use delta time. Unless you're just starting out, in which case it might be overcomplicating things. You'd use delta time because the core mechanic of the game (earning money) is directly linked to the time elapsed, so keeping the game in sync with actual time is very important.
This:
Or is that lag just voided steps and the variables will pick up where they left off with no differences?
is answered by the answer to this question which is:
3. Is lag kind of like a pause? When the game lags, it stops code until it catches up?
Yes. It will never skip a step (unless you have hardware failiure, and then you have much bigger problems). It will either keep ploughing through the code or stop entirely. And that's the reason you want to write code using delta time.
Once the code realises that more time has passed than it has time to render for, it calculates how many steps
need to be skipped in order to catch up. Then it increments all the variables by their usual amount
multiplied by the amount of steps it skipped, RATHER than going through those steps incrementally and inevitably ending up further behind.
4. Is there anything I should be aware of while making an incremental/click based game?
Still assuming you mean a cookie clicker game here. Most cookie clicker games are somewhat procedural and just use maths to work out the prices of things. When you buy an upgrade, it would increase its price by say 20%, rather than have a list of predefined prices.
And this 'lazy' method extends to the individual upgrades themselves. All you need is a list of upgrade names, and then all you need to do is give an initial price. From then on, every type of upgrade will cost say 150% more than the last.
So TLDR:
The more you earn, the more expensive the items you want become. It feels like you're making progress but all you're doing is shifting the goal posts. At the beginning of the game you make $1 per click and your upgrade costs $20. At the end of the game you make $1,000,000 per click and the upgrades cost $20,000,000. It's just very simple scaling maths, and if you implement it like this it will save you a lot of time.