Let's separate the issues.
About the specific Avast edition you have: there are 3 downloads available for home users. There are 2 trials (Avast Pro and Avast Internet Security) and there is 1 Avast Free edition. All of them need some kind of registration after 30 days. For the trials, you need to pay and register to continue using them. For the free, the registration is necessary about once a year, but it's free.
You need to be sure which specific edition you are downloading, since the setup.exe files are different. In short: do not confuse the "free" trials with the Free edition of Avast (this has happened before to other users).
About the space needed, about 160MB sounds about correct. The needed space is not a fixed number, and it varies depending on the installed shields, the reports, the logs and for each database update.
Once in a while, Avast cleans up itself, deleting old databases and downloading a new "complete" one (instead of "patching" little chunks of the current database). This is a way to balance downloads and needed space.
Some size's limits (for logs for example) are easily configurable from the main GUI of Avast.
The original setup.exe download may be smaller, but after updating the database, having 160MB is not at all shocking.
Now, about the removal utility, for you to remove completely old versions and editions of Avast you need to select the correct folder and the correct specific edition of Avast from the list in the removal utility. Run it from Windows Safe Mode, and reboot into Windows Safe Mode again to run it again, selecting each time a different version/edition.
For example, if you had Avast Pro 5.x and then updated to Avast Pro 6.x, then you need to run the removal utility twice, with reboots in between and selecting each time the respective edition / version.
Once all is removed, check the "normal" folders so to review if they are really gone, and if not, run the removal tool again, selecting the correct folder. Reboot into Safe Mode between runs.
You can select the correct edition of Avast ("Avast Free", if I understood you correctly) from the official website and download that. Install it with Administrative Permissions so to reduce potential conflicts.
Reboot immediately after the installation finishes, and only then start its configuration or whatever else you want to do. Don't skip that first immediate reboot.
