I'm not sure I fully understand your question, but I will give you the basic equations which are pertinent to your questions:

Energy Balance

For sensible heat transfer:
M x Cp x (Ti-To) (hot fluid) = m x cp x to-ti)(cold fluid)

For cold fluid boiling:
M x Cp x (Ti-To) (hot fluid) = m x cp x (tb-ti) + m x latent ht (cold fluid)

where tb = boiling temperature and no superheat is added to the vapor.

Q = M x Cp x (Ti-To)

from energy balance (any of the above equations will give you that)

Heat Transfer Evaluation

Q = Uo x Area x LMTD

where Uo is the overall heat transfer coefficient of the exchanger and is determined by the velocities of each of the fluids and geometry of the exchanger. Area is determined solely by geometry and LMTD is determined by both geometry and fluid inlet/outlet temperatures.

Please refer to standard heat transfer texts and/or Perry’s Chemical Engineers Handbook for specific methods of determining heat transfer coefficients for the hot and cold sides.