Standalone InstallationYou have the option of installing Biztalk360 on a Biztalk server or as a standalone. A standalone installation will require that you install some Biztalk components and get your accounts and permissions right, in theory. In practice you'll find that various parts of Biztalk360 will not be functional. An example of this is if you use custom components in BRE, then BRE will fail to load. You'll then need to install the custom components on the standalone server. Another example is an inability to start/stop an application due to a bug in the Biztalk installation. Most of these problems can be avoided by installing on a Biztalk server as all the assemblies you need will already be gac'd.
Although it seems counter intuitive to put your monitoring tools on the system that will be monitored, you can let your system administrators use their monitoring tools to monitor the basic system and database availability and let Biztalk360 monitor the rest.
TL;DR avoid the grief of installing Biztalk360 as standalone. Install it on your Biztalk server instead.
BAM and ESB Portal
Both BAM and ESB in Biztalk360 are no-where near feature parity with the existing web sites in terms of functionality or usability. A pity since we use these features heavily, although I hear that there are updates coming which will close this gap. I think this is one area where Biztalk360 can really shine as the existing BAM & ESB portal are really dated, but nobody has the time to re-implement these to do a better job. I still find myself using the existing solutions because they are still better in most ways. I think this will change soon.
I've had a few problems with monitoring due to permissions related to the service account in use, but other than that it has been smooth sailing. The fine grain monitoring is excellent and in particular I love the process monitoring which allows you to check that a process has run and alert you if it hasn't. Massively useful for things such as daily processes.
I've had to call on support a few times and they are a pleasure to deal with. No problems here.