Think of information as if it were honey, the sweet substance bees produce, not the synonym for "nice person" or "sweetheart". Also think of it in its flowing state, not crystallized.
How many honey does the recipe call for? ungrammatical
How much honey does the recipe call for? grammatical
How many informations on your web browsing habits does Google collect? ungrammatical
How much information on your web browsing habits does Google collect? grammatical
An amount is an unspecified quantity. For that reason we cannot ask How many amounts...? because nobody knows the size of the amount. And when you add amounts together, they simply become a larger amount. An amount has no size until it is modified, for example "a small amount" or "a large amount", and even then the size is relative and vague.
The word staff is what is called a collective noun, which is a noun that denotes a single collection of countable objects. As such, it may be treated as either singular or plural (uncountable or countable), depending on context.
You treat it as singular/uncountable when the entire group of included individuals are doing the same thing:
The staff meets every week and reports on their status.
You can treat it as a plural/countable when different individuals within the group are doing different things (even though the noun itself doesn't take a plural form):
The staff specialize in a variety of disciplines and are assigned to different tasks.
(You'll also find regional differences - British English is much more likely to treat collective nouns as plural than American English is.)
In this latter case, you could imagine that this is using "staff" as a synonym for "staff members" and there are a few (but far from all!) collective nouns where the collective noun can be used idiomatically to mean a member of the collection. The ones I can think of, for whatever reason, generally refer to groups of human workers, so maybe this grew out of what is sometimes pejoratively called "management speak."
So you see constructions like this:
There are only a few overnight staff on duty.
All personnel evaluate each other's job performance.
Half a dozen crew are required to staff each shift.
Again, this last usage is not universal for all collective nouns. Most collective nouns do the singular/plural thing, but do not accept this last idiomatic use as a synonym for "member of the collection."
For example, if you're talking about a flock of birds:
The flock lands on the lake's surface. (correct use of singular/uncountable showing a collective action)
The flock scatter in every direction when a predator appears. (correct use of plural/countable, emphasizing that each bird goes in a different direction)
A few flock stay behind and one is caught and eaten. (incorrect - sounds very unidiomatic)
Best Answer
The first part of your question is exactly right: too much money, too much water, too many dollars, too many lakes.
As for "I have too much time" – by itself, that means something like, "I have so much free time I don't know what to do with it." So, I'd say that part of your question is correct as well.
The last part is where things get dicey. "I have a lot of time" (which could also be phrased as "I have plenty of time") generally means "I have a lot of available time," and that could be for any number of reasons – it's context dependent. I would think that any of these questions or comments could be answered with, "Yes, I have a lot of time":
Thanks for helping me fix this lawn mower; do you have enough time to help me fix the wagon, too? (In other words, Do you have any remaining available time right now?)
I was wondering if we could set up a meeting sometime next week. (In other words, Sometime in the future, will you have a block of available time?)
Our football team needs a treasurer for the upcoming season. Could you volunteer? (In other words, Do you have enough available time that you could take on some short-term responsibility?)
Could you take on a second part-time job in the evenings? (In other words, Does your schedule have enough free time that you could take on another activity on a regular basis for the foreseeable future?)
And then there's the context you mentioned, where the answer might be "No, I have a lot of [free] time":
So, "I have a lot of time" can mean several things, depending on the context.