If you experience any problems (server errors, connection, etc.) with the download and installation of components as in your three images then part of the installation is going to fail, which may result in a complete failure to install.

I personally would never use an on-line installation, for several reasons:

  1. If you are doing this and you have another AV installed, then avast has to do things to delay the installation until the current AV is removed.
  2. If you have already removed your current AV then you are going on-line without protection. Some say the risk is small but I feel is is still a risk.
  3. It would appear that using the on-line installer it takes longer to download the components, that it does to download the full off-line installation file.
  4. You can keep a copy of that full off-line installation file, should you need it in the future.