My mom 58 years old take methotrexate for her rheumatoid arthritis disease and ibuprofen (everyday) to relief joint pains is this safe ?

Probably: Methotrexate and Ibuprofen have been around to treat RA for a long time. With Methotrexate i monitor patients every 2-3 months with blood counts and liver function tests. Ibuprofen is an nsaid. Kidney function and blood pressure need to be monitored every 4-6 months. If she has underlying liver or kidney disease she needs more frequent monitoring as then the risk of side effects increase.

Yes: This combination is usually safe. Routine lab tests are done to screen for any med toxicities.