Yes, it is possible to use "ever since" with the present perfect. "Ever since" links two events, a cause event and something that is true from that point in time onward. This is actually ideal for the present perfect tense because one of the uses of the present perfect tense is to indicate that something which began in the past is still relevant in the present. An example of this use is your sentence:
"I always thought it was wrong, but ever since I read it, I've been more confused."
Using the present perfect with "ever since" shows that the speaker has been and is still confused by something which they read in the past.
With the past simple tense, as in your last sentence, it would be more appropriate to use "once" instead of "ever since". This is because "once" links a cause event with something that changed, but does not necessarily link to the present.
Once I did that, it stopped bothering me.
This sentence shows that the speaker was not bothered by "it" as soon as they did "that". It however gives not indication of whether this continues to be true in the present.
I saw your edit, if I understand right you meant to ask if it is possible to use "ever since" and present perfect without past simple, which would look something like:
"ever since" + present perfect + present
Ever since I have been pregnant I feel sick each morning.
The answer is no, this is not natural English. This structure may be encountered in informal English, but it is more natural to have the structure:
"ever since" + past simple + present perfect
Ever since I got pregnant I have felt sick each morning.
EDIT: If the perfect solution is hypothetical, and can't exist in real life, we describe it as a 'Holy Grail'. Here are a couple of examples:
- We won't ever finish our project if we keep trying to invent a Holy Grail for our customers
- I know you want to hire a doctor who can also perform surgery, but we've refused a lot of great interviewees in our search for the Holy Grail.
Also : Panacea
It literally means 'a medicine that cures every disease', we sometimes say cure-all instead of panacea because it's not a very common word. Here's an example:
He wrote his own accounting program as a cure-all for all the money problems his company was having.
Panacea is for when your perfect solution is real and works.
Best Answer
"Do you have the time?" would be used to ask what time it is currently.
"Do you have time?" would be used to ask if the person has time in their schedule.
To the best of my knowledge "Do you have a time?" is not used at all, at least in standard American English. It can however be used as a phrase in a larger question (as graciously pointed out by J.R.). An example of this could be "Do you have a time of the year you prefer?"