intermittent starting problems and other issues

First off ths is my first post here and am new to the protege5 but have been in rx7 scene for a few years. I am having issue with starting. I turn the key and there is nothing, no clicks from the solenoid just nothing. sometimes if i hold the key in the start position it will start cranking after a few seconds. other times it delays and then cranks slow like a low battery. it occurs first start of the day and when the car sits for long periods of time and is kinda of cooler out. I suspect its not a battery issue cuz it would cause the solenoid to just click becasue there is not enough voltage to keep the solenoid opened. am i wrong? where should i begin trouble shooting? this might also be related but the second issue is dimming head lights. while crusing mostly and at idle. they just dim for a brief seconf and then back to normal. also noticing the interior lights dim and i can hear the blower motor slow, idle doesnt drop when dimming but idle does jump when the the lights brighten back up. Possible alternator? What should a voltmeter on the battery read with the car running, the rx7 is 14.7v? same? Im going to check and see if the voltage drops out when this occurs. and lastly is the damn sport auto tranny, im noticing that fron a stop the rpms go up to roughly 1500 and there is a slight hesitation and then acts normal. it does this in drive and manual. the 7s have a hesitation when the secondary injectors and aux ports kick in, and is normal so is there somekind of system that is causing this, or the TCU(i know its some how electronically controlled) trying to process what its doing? Car is an 03 p5 with no cel lights or codes. all issues could be linked but i dont know, its really the first time i owned a car this new and is miles ahead of my 7 knowledge. thanks in advance and sorry for the long post.