Would an electrician do this for me for free?

If it is an estimate/proposal to do the work, then most will do that for free.

If you are looking for someone to come in and show you how to do the job, then you will probably have to pay for that. (My knowledge and expertise are free here in this forum. But not if I have to come to your home.)

If you are considering buying your own material...I would not recommend it. I have have dealt with this before. Every time that I have to work with the crap that is usually sold at the big box stores, I usually have to spend twice as much time on it. There is almost always something missing (that I now have to hope I have something comparable on my truck) or it is not the most efficient way to do the job. Also, most good electrical contractors can buy at wholesale, put a mark-up on it, and still sell it for the same or less than you can go buy it. The big box boys will sell wire and conduit dirt cheap. They call this a "loss leader" They are willing to take a loss on that stuff. The reason...They know that they will bend you over on all of the fittings and such that they know goes with it. The last problem with this is a warranty. If my customer wants to supply the material, no problem. I am always willing to install whatever the customer provides (as long as it meets code). But, if it fails, they are on their own. My boss doesn't guarantee products that we did not supply.

As well noted already, what may take you a couple of days to do may be done by a pro in a few hours. You can have the satisfaction of knowing that it is done right.

Also, in most jurisdictions, you can do your own work on your own residence. But, you are not exempt from permit and inspection requirements. Failure to follow the rules can have consequences later (such as trying to sell the home or file an insurance claim after a fire).

What would you be consulting him about? Do you mean that you want to pick his brain about how to do the job without paying for his knowledge? I suspect the answer is no, and if he has an hour minimum charge as many of them do, it will probably cost the same to consult him as it will to have him do the whole job. He'll do it faster than you will too.

not the electricians i know they will not risk their license with you running the wires if you do it wrong and there is a fire its on them

Trying to save money is very admirable, but I fear you are close to being "penny wise and pound foolish".
May I suggest the following?
You seem to be comfortable with installing the fan (with light?) and the vent that goes with it. So go ahead and do that much.
You mention "hook it up to the electric panel" which leads me to assume this is a new bathroom. Right?
It is entirely possible that this small additional load can be added to an existing light circuit.

At this point my suggestion is to let the electrician supply the wire and skill to install it to code. Company's do give free estimates but if this is all the electric work you can think of at this time just ask for the hourly rate. This amount of work (as I think it is) will likely be more than 1 hour. How much longer I can't say with any accuracy.
An additional bathroom can add value to a home when done to code, and can cost you money later at the time of resale when not.

Hence my earlier quote.

Now then if you really want to do more...

If there is a light or junction box close by, determine what size fuse/breaker controls it. 15 amp = #14 wire and 20amp = #12 wire. Depending on your location you will need either Romex or MC cable. Building supply/hardware store employee should be able to tell you which. Strap it within 12" of the panel and box, and every 4' after that. Leave enough wire at the panel to reach the bottom and half way back up to the top of the panel. Leave at least 10" at the switch and fan(light).

Understand that the electrician will likely note on the receipt that you supplied this and did that.

Please give consideration to having all of the wiring done by a contractor. (support your local economy)
Best of luck!

i don't know the wiring rules other than the ones in aus but a licenced electrician needs to sign off on all the jobs they do so if you ran the wires he's going to want to check it anyway otherwise he's leagaly responsible if you did something wrong (wrong gauge wire or if you run them somewhere your not ment to) so my advice would be first chat with your sparky.

Call a couple of local contractors and tell them what you need and see if they will come out and give you a price...

yes they well...i hooked up a compressor did all the wiring and put in the braker and i just wanted them to just come look at it and tell me i did it right..so i new it wouldnt start a fire.and they wanted 70 bucks just to come over

call around to local electricians...state certified ones. Ask for quotes theyll come in and see the project you have and give you a price tag, and might tell you what it entails. Also you could see if you can have an exchange of trades. Im an electrical engineer, and I can design electrical systems and Sign that they are valid, Just call them up and ask for what you want.