1) Am I able to list topics on my home page rather than categories. And or have both; where I have categories listed in a small section, but have the focus as topics.
XF allows you to set any route as your index page route and there is lots of flexibility in terms of being able to add widgets to various places. As an example of the latter one,
The Admin Zone adds a widget containing new posts at the top of their forum list.
2) If yes, besides topics shifting positions based on latest posted or most popular, can I manually add and remove topics on the Front Page as I wish
We do have a new widget and a new feature coming in XF 2.2 called "Search forums". A search forum is a forum which can aggregate threads from multiple forums on your site based on the criteria that you select. That may work for you.
3) Is it easy to modify my Home page like uberpeople.net where I have pictures highlighting and linking to selected topics.
This looks like it's coming from an add-on. I'm not entirely sure but I think it's "Featured Thread Slider" which might be this one but I strongly recommend searching around to find something that meets your needs:
Warnings Don't upgrade this add-on with old version (File directories have been changed.) What does this add-on do? This add-on shows to featured threads with responsive slider. What's New Add-on has been updated with support for XF2.1+ Added...
xenforo.com
4) is the $160 payment annually or 1 time.
You pay $160 one time. This gives you support and unlimited upgrades for 12 months. After that 12 months you don't need to pay anything. You can carry on using the software. But at a point where an update is released that you want or if you need support then you would have to extend your license. The license extension costs $55 for an additional 12 months.
5) After payment, when you go in to install the script on my selected host- does my forum come up instantly after that?
Once you have paid, the software needs to be downloaded and then the files uploaded to your preferred hosting provider. You need to buy and point a domain name at your host. You will need to create a MySQL database in your hosting for XF to be installed into.
You then visit the install page and follow the instructions.
If you want us to do the install process for you (you still need to arrange a host, domain name and create the MySQL database) this costs an addition $50.