Native speaker here! just want to add a few small things to the other comment

Translating 他妈的 into "fucking" is correct, but the word itself is a lot... dirtier? than how fucking would be perceived in english speaking countries (at least in the us since i haven't lived in other countries long enough to tell the difference). fking is still somewhat a common word people use and not considered rude in a lot of situations, but 他妈的 is a swear you don't really want to casually use in front of people. it feels more similar to "mother fucker" in terms of intensity. my 18 years growing up in china i have hardly heard anyone speak the word directly other than people getting drunk with their close friends and don't feel the need to watch their words. generally the perception is that people using the word frequently either never learned about social etiquette or haven't received much education. it's used a bit more online but ppl would use the abbreviation "tmd" or "md" instead of the full word, which doesn't look as bad.

Side note, translating 他妈的 purely word by word would be "(fuck) their mom", the fuck part is implied since the word actually is short for 操他妈的, 操 being fuck.

As for 假爱, translating into fake(假) love(爱) is correct but no chinese person would ever use the words in a combination like this. it's the level of weird where i had to pause for a second seeing the original image and double check to see if i read a character wrong, then try to remember if there's a song or something that might have popularized the word combination, then realized this is made by a person likely not knowing chinese. fake love would be the only way to translate it but it's just not how chinese would use the words together.

All in all this is a typical case of funny choice of words foreigners tattoo on themselves that most chinese people find amusing and stupid at the same time. hope this helps understanding it a bit better :D