I've tried all of the methods you mentioned.
1 Give my user id and password with complete access
I would lean away from this option as it not only gives access to everything but also limits your future options for what you can send to this account. Its also complicated when you and your assistant part company.
2 Create a new user id and password user name of PA email@example.com and forward only delegated mails
This is not a bad option but still not my favorite. The biggest issue for me was when my assistant moved on, even if I retained the account, it was in someone elses name. Which means that your next assistant would need a new account. Not too big a problem if all you do is forward emails. But if you have filters setup with forwarding rules (like in Gmail or Outlook) you will need to change all of those when your assistant changes.
3 Create a new user id and password with common id firstname.lastname@example.org and forward only delegated mails
This is my personal favorite. Since you are using the company name you are less likely to end up in a dispute over whose inbox it is when your assistant leaves. It's also easier to use in a client-facing manner because they can associate the address with your company.
To make this option even better, I use it with aliases (as recommended by Aymeric). Aliases allow you a lot of flexibility in how you setup your flow of emails. In some email software you are able to put two addresses in for an alias (or a list) which allows you to setup an email "channel" that goes to both you and your assistant. I've found this very helpful in some situations.
One other issue to consider here is historical data. Your assistant will likely be receiving responses from clients, vendors, associates, etc. You want to make sure you can retain all of this data for reference and possibly auditing. If you change email addresses repeatedly you will need to figure out how to transfer or backup your old inbox each time. So this is another good reason for retaining the same inbox.
Also, keep in mind that many email clients (including Gmail) can check additional email addresses that you configure. This provides some additional possibilities that would allow an assistant to have an independent account that pulls emails in from your central PA account. If you consider this option you will want to use two important configuration options. 1) "Send As" which will allow the assistant to Send Email as though they were sending from the central PA account (or even your own account), and 2) "Leave Copy On Server" which will leave a copy of each email message even after your assistant downloads them into their individual inbox.
1 Give my user id and password for dropbox and google docs
Again, for the same reasons mentioned on #1 in Email Sharing, I think this is the least attractive option. It is simple though. Worst case I suppose you can just change your password when it's all done. I prefer options that afford more control, consistency and flexibility, especially in the event of a change in your staff.
2 Create a new a/c for PA for dropbox and google docs and share all files with him
In a general sense, for file sharing, this option would work as well as the central account. It keeps you in control of the access. If there is a change in assistant you can easily get on and change the access for the PA account.
3 Create a new common a/c for PA for dropbox and google docs and share all files with him
As with email, I like this option the best. These common accounts are also good in the event that you sell a business. They are much easier to transfer than when you are using a personal account.
Also, on Google Drive, use the share folder option. That way all files under that folder are automatically shared with your assistant.
Side Note: If you use DropBox, consider signing your assistants up with your affiliate link. This adds free space to your central dropbox account. ;)