Installing Flash from Schwab.com

Also, since you're probably stuck changing passwords and cleaning this up, this would be a great time to enable two-factor authentication on important accounts like your email and financial services.  You would also be wise to switch to a password manager that will create and keep track of unique passwords for each site that you use.  That way, if a site you used is compromised, you don't need to worry about those credentials exposing all of the other services that you use.

There's a good list of options here:

Best Password Managers of 2017 - LastPass vs. True Key vs. 1Password

Finally, if you don't have backups, you might look at enabling Time Machine on Mac, and/or using a third-party cloud service (off-site backups are great defenses against fires and ransomware).  There's a list of services here: https://www.cloudwards.net/cloud-backup-for-mac/

In all likelihood, it sounds like you were tricked into downloading malware designed to impostor a legitimate Flash Player download.  Unfortunately, because Flash Player is ubiquitous, it's a great choice for bad actors looking to get you to install something.  As technical controls become increasingly difficult to exploit, attackers increasingly focus on human factors, which are easier to trick.

Given that you were working with important financial services at the time, you might want to take a few minutes to go find a clean computer and change the passwords for that and any other important services you might have used since performing that installation.

Once you've done that, you should probably think about reverting the machine to a state prior to doing that installation.  If this is a work computer, I'd recommend talking to your IT department today.  If this is a personal machine, and you've got Time Machine (or some other solution) backups, that should be a straightforward exercise.

If you don't have have good backups and it's your personal machine, you have a bit of a mess on your hands; however, if you're using that machine for accessing important services like banking and healthcare, it's probably wise to deal with the problem.  The most thorough approach would be to copy off any important files, then just wipe the machine and reinstall MacOS.  If that's intimidating or particularly ugly, you might want to seek out expert help on that front.

No.  Official Flash player installer will not modify the user's home page, nor install a booking.com app.

When you were prompted to download/install, were you in an area of the schwab.com site that requires log-in to access? If not, please provide the link to the exact location where you were prompted to download/install Flash.

Thank you.