Learn Spanish (Latin America): Un minuto tiene sesenta segundos.

Yes! You could say Hay sesenta segundos en un minuto. Both ways are perfectly natural, but using tener (to have) is a very common way in Spanish to state facts about what something contains, literally meaning 'A minute has sixty seconds.'

I always mix up sesenta (60) and setenta (70). Is there a trick to remember which is which?

This is a very common A1 mix-up! Remember that sesenta (60) has an 's' in the middle, just like seis (6). Meanwhile, setenta (70) has a 't', just like siete (7).

Are time words like minuto and segundo always masculine?

Yes, minuto (minute) and segundo (second) are masculine words, which is why we use un before minuto here. However, the word for hour (la hora) is feminine. That is why we always use the feminine article las when telling time, such as son las dos (it is two o'clock).

If I want to tell the time and say 'it is 4:01', do I use the word minuto?

Generally, no. When telling time on the clock using son las..., you just state the numbers. 'It is 4:01' is simply Son las cuatro y uno. You only need to use the word minuto when talking about a duration or a quantity of minutes, just like in this sentence.