If Avast! had a real toolbar, wouldn't you think it would be included in the installer as an option? The very fact that there is no such option plus the fact that this toolbar is offered by an outside source makes it suspicious right off the bat.
Avatar FX6327X Desktop, AMD FX-6300 6 core CPU, Radeon R9-270X graphics, 8GB RAM, Windows 10 64 bit, Panda Free AV, MBAM on demand
HP6140 Laptop, AMD A8-3500M Quad Core APU, 6GB RAM, Windows 7 Home Premium 64 SP1, Panda Free, MBAM
Google/Asus Nexus 7 tablet, Qualcomm Snapdragon quad core 1.5ghz, 32GB storage, Android 6.0, Dolphin browser, Bitdefender Free All machines behind a NAT router