Could it be the rest of the contacts have been synced to Google acc ? When reading the thread first time, I didn’t realize your phone was functional, apart from cellular services. Just export contacts to Mi acc from Contacts settings. Also make sure to force backup for everything in Setting/Backup.
Make complete uninstall of Mi Suite, it’s complete PoS and will probably interfere with 3rd party software flashling attempts. Having Google services (Play Store and supporting software) is no problem at all on Xiaomi if using custom European rom. It’s the same thing as official Chinese (not custom as, for example, Cyanogenmod), but with bloatware and Asia specific apps removed. Translations are much improved and Google apps are bundled. As a bonus, you get rom update every friday. It’s also based on Miui 8, while you are still on version 7. You just need to install Xiaomi drivers bundle and Fastboot. After initial setup, it takes 15 minutes to flash phone. You will also be able to perform any future updates from phone itself, no PC involved, and will have recovery mode available for making complete backups. Just tell me your Windows version to give you proper links.
I am using WIN 7
I thought this was official european/global rom! without chinese crap.
Yeah, it's global, but with room for many improvements, filled by xiaomi.eu rom. I have used official global very briefly, and all I can say euro rom provides much more consistent user experience. There is a list of changes on the bottom of this post
Follow this to flash latest Chinese rom (download latest china developer for your phone), which serves as base for euro. You then need standalone fastboot to flash recovery, which will be used for flashing euro and future updates. I'm going to assume Mi Flash Tool includes drivers needed for fastboot. If it doesn't recognize phone, I'll upload you zip I've used, I'm not home now and can't find exact package. Download xiaomi.eu rom and recovery here, you want weekly. Recovery is in the zip, extract .img file and copy it to the installation dir of fastboot. Open cmd as admin there, boot phone to fastboot and run *fastboot flash recovery recovery.img*. After it finishes, reinsert battery and boot to recovery (same way as fastboot, just volume up instead of volume down). In recovery, enable system modifications if popup asks you, wipe all partitions (advanced wipe option), then copy euro rom zip to phone (enable mtp in recovery settings if it's not visible on pc). Select zip from install menu, flash it and reboot to system. Ignore offer to root phone, if you need root, there is zip to flash next to recovery download link. This should do it, next updates are simple zip flashing from recovery and wiping cache/dalvik partitions only.
Please check your google account and see logged into gmail if your contacts are there when you click “contacts”
Guis, sorry for leaving you without any feedback,
so, just and update on this issue and what I think was the problem:
when I bought the phone it had some chinese rom installed by the seller, of course that did not do the job for me so after some experimenting I managed to update the phone with official rom, that worked OK, no issues from then, unfortunately new rom (V7.5.1.0.MXDMIDE) was apparently not designed for china phones and it probably offered me to install it because of previuos version that was also international but worked OK.
To cut the storry short, guy that I met at local IT forum was helping me to flash different roms from fastboot and after 4 hours of not getting anywhere I just mailed him the phone and after several days he was able to fix it. I also had to replace my SIM card.
Costs of repair: ~15€ (thanks xiaomi)…
Seems you're glad to have worked out the problem, Sirius9. Got your phone rooted? If not, maybe you could have asked the IT guy to do it for you; being root allows you to actually take control of the god@#$%ed thing and provide solutions to problems you are restricted to in non-rooted ROMs. And of course, if you don't want to actively use your root privileges you don't have to, and it can't hurt you to have them if you are wise. :CROWN:
As an user of an XT1032 (euro 2013 Moto G), all I can say is I really ended up disliking the lack of control a user has without admin rights on, well, modern computers in general (Android, Windows, etc); that “take this and screw you” approach/policy of SSOO makers. So, I picked up the reins and installed an optimized rooted ROM on my device (one based over a stock one), and it's been a real blessing since then. Without bloatware, forced “updates” and giving up on the stupid idea of updating whatever apps “just for the sake of it”, you can really go no wrong with it. 
Of course, I must admit I've always been a computer guru, but that's another story. 
Cheers ^:)
No, I am on the official V7.5.1.0.MXDMIDE, was left almost 2 weeks without the phone with that “yes sure, update it” incident, when it comes to phones I am now more on “if its not broke don’t fix it” stand.
I guess I was late to the party but the way I fix this problem was to just use the developer rom
the global ‘stable’ rom wasn’t as stable as I expected.