You can install mojoPortal in a sub directory and run it from a sub directory but you cannot make it pretend it is a root site by url rewriting, the sub directory will be part of the url.
Also the /Data and /App_Data folders beneath the root must be writable. If that is not allowed by your host then your host does not meet the hosting requirements needed and I would advise you to get hosting somewhere else.
Even a host telling you that you must run it form a sub folder and use url rewriting to make it look like a root level url instead of just installing it in the root is just ridiculous.
I have no solution for those constraints, the host should work for you not against you, you should get a new host in my opinion. There are lots of good hosts in the world who will not impose such silly constraints.