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There is no specific cut off unless she starts her menopause (the time when women stop having regular periods). As you get older there is a small percentage reduction in chances of getting pregnant but at 35 in a fit healthy woman there should be no problem in general.
If she’s having irregular periods often she should speak to her GP so secondary causes like thyroid issues can be excluded
By fertility tests do you mean ovulation tests?
There are many different brands that sell fertility kits, overall they should test the LH hormone levels which indicate ovulation this is reliable however I cannot confirm the accuracy of specific brands
I would advise your partner to use an app to track her cycle, so she can monitor her period and fertility window. Indeed you can use ovulation kits to help tract them cycle if you wish to do so.
I would just recommend regular intercourse and cycle monitoring, If there are no underlying health concerns, 80% of couples fall pregnant within one year. If that does now happen you should see your GP for further testing.
Hope that’s answers your question, wish you all the best.