Does call option delta equal put option delta plus 1?

Put option delta = Call option delta - 1

Now you solve for Call option delta in terms of put option delta!

Yes.

call delta is approximately N(d1)

put delta is approximately N(d1)-1

Does call option delta equal put option delta plus 1?

Put option delta = Call option delta - 1

Now you solve for Call option delta in terms of put option delta!

Yes.

call delta is approximately N(d1)

put delta is approximately N(d1)-1