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That is the build number.
The major number 17763 stays the same for the life of your version, in this case 1809.
The minor build number .775 tells you which cumulative update you have, in this case it's the one from October 3rd.
Cumulative Update KB4524148 Windows 10 v1809 Build 17763.775 - Oct. 3
There is a later update to 17763.832 but as it has no new security fixes it is entirely optional. It won't install automatically. Basically it's telling you that you are fully up to date. You have 1809 with the latest update that you'd expect it to have with windows update automatically installing updates.
Tools no, not that I'm aware of. But they do have a list of known issues.
Known and Resolved issues for Windows 10 May 2019 Update version 1903
Look at the issues described as 'Investigating' or 'Mitigated'. For any that would seem to apply to your machine, click the 'See details>' link. This will tell you which version(s) of the driver or software has a problem and say something like "...we have applied a compatibility hold...". Hopefully you'll be able to find what needs updating.
Probably not, but it is always a sensible precaution to make a system image with something like Macrium Reflect Free before any major upgrade.
You could run the MCT, use it to download the ISO, mount that and run Setup to start an upgrade.
Alternatively you could run the MCT and use its 'upgrade this PC now' option, that akin to using the Update Assistant. Or you could use the Update Assistant itself from here: https://www.microsoft.com/software-download/windows10
Of the available options, the Update Assistant should be the safest to try. I understand it makes more compatibility tests than when using the ISO.