No you don't need other version it will not make a difference.

There are many new items and you need to fine tune.

see these manulas for the most items: https://helpcenter.websitex5.com/ru/post/154023

Why it is messed up and how is difficult without a website adress of picture, because I don't know what you have in v10 and how it looks in v13. That can be for every project a bit different.

You could set responsive off, but that's not why you have v13. In v13 you need to set standard 4 viewports for the responsive to work as you wish. X5 try's to do as much as possible for you but it won't be perfect. Also it could be that templates where too old for the new designed features that they have been replaced for other reasons, so it could be that you need to set that also.

Well best is too walk through the convertions manuals, it's a big step from 10 to 13 so you need to make some adjustment from every version and skipping 2 versions could mean even more adjustments.

Just sit back for it go through the manuals, if you have more questions then please provide actual examples. It will help us giving you better and directer answers.

Thanks.

Hi Mike, 

please follow the link Andre has given you: it is a guide about how to import a project into WebSite X5 13 correctly. Please consider that the software has gone thought some versions and changes, so that it is possible that you will have to edit the project a little. If despite having followed the guide you are still having difficulties, please provide me with some screenshot, so I can see what's wrong and tell you how to proceed to fix everything. 

Thank you. Kind regards.