I am using my father's guitar, and it's pretty old, at least 25 years, or more. The tuner pegs are rusty. I sent my guitar to a music shop weeks ago, and he helped me to restring already. Later on, the strings are out of tune. I do not have the plan to buy a new guitar now, probably gonna stick to this guitar till next year. Is it safe to tune (tighten) the guitar with the tuner pegas rusted?
The going out of tune is rather common on a lot of guitars - especially when new strings are settling themselves. Rusty metal against rusty metal isn't good, so first move would be some lubricant, worked in to the meshed parts. That may be all you need.
New machine heads are easily fitted, but look out for screw centres the same as the old ones; barrel length and diameter the same, and either 6 the same or 3 a side, to be a direct fit onto Dad's guitar.
If the guy who restrung it thought it needed new machine heads, it'd be surprising if he didn't attempt an extra sale.