Ubuntu Networking :: Seamless Ssh Through Intermediate Host?

My situation is that I've got a home connection, with a router that my ISP won't let me access (to forward ports etc), and all incoming ports blocked as far as I can tell. I would like to be able to get around this and allow incoming ssh connections to a home PC. To facilitate this I've got an (user) account on a remote shell account, which does not have all its ports blocked and which I'd like to use as an intermediate to ssh into my home machine.

What I've managed so far is to ssh into the shell account (let's say it's on intermediate.host) and tunnel a port back to my home machine (let's call it home.host) by running the following on home.host:

ssh -fNR7777:localhost:22 myuser@intermediate.host

Then, I can ssh into my home machine from the shell account with a simple:

ssh -p 7777 myuser@localhost

OK, well and good, in principle I can then ssh into the intermediate from anywhere, and from the intermediate ssh into my home machine. BUT, I'm curious if it's possible to make this a seamless procedure so that if I connect on a particular port to the intermediate, it simply puts me onto the home machine directly (with appropriate ssh keys in place, of course.)

One reason is it would be more convenient. Another is I would like to be able to make sftp connections to the home machine from anywhere, which I don't see would be possible with the above method. Still, it should be possible, right?

So three questions basically:

1. Can I somehow make the connection to my home go seamlessly through the intermediate host?

2. Can I do this without root access to the intermediate? (I've only got a regular user account there.)

3. Is there any way to do this so that another person could reach my home machine (say for sftp access) without giving him my login details for the intermediate host? (I would create an own account on the home machine, obviously.)