#1
Say the count s 1 and, 2 and, 3 and ,4. or

1, 2 and a, 3 e and a, 4 e and a.,1


See I have to sing on the highlighted beats. When I'm playing guitar with these kind of rhythms I don't have any trouble,I guess because I can count out loud plus I have upstrokes and downstrokes to help me.

But how am I supposed to sing in time when melodies are heavily syncopated?
#3
Instead of counting out loud, try counting in your head. Also, try getting someone to clap on the beat and sing on the off-beat, so you can get a feel for it, then try it without the other person.

It is about practise, so if you really want to do it then practise it a lot. Also, listen to lots of music that has this sort of stuff in it or (if possible) a recording of what you're supposed to be singing.

Although i try and stay away from very ambigous statements like this, i think you should try and feel the music. Listen out for which instruments play on the beat and wich on the off-beat, then you can use it like you did the clapping or sing at the same time, respectively.