to detect Flash player in your visitor's browser, and to save me about half and hour's typing click here for information on how to do that.
2. Please don't bother with visitor counters, they are so naff, and mark your site as 'amateur'. In any case, they don't tell you how many visitors you've had, they simply record the number of times a page is visited - which is an entirely different thing. Put the counter on your home page and it will click up each time anyone visits that page - one person can record several times as he/she clicks around the site. If you have the site hosted with a 'proper' web-hosting company you'll have a control panel, in which you should be able to see proper server log statistics.
3. You can teach your client how to use DreamWeaver, but he'll need to buy it and install it on his machine - hardly a justifiable expense for one site. Alternatively you can use a Content Management System, which will enable your client to add content without disturbing the page layout.
There are various software solutions, but some of them are pretty expensive. click here for one that may suit you, or click here for information about some more.