Weak Pull-Up's

A WEAK PULL-UP is basically a RESISTOR built into the internals of the PIC that can be switched in to sit between an I/O pin and Vdd (+5v usually).

It's called a WEAK Pull-Up because it can be anything between 20K and 250K... Some Datasheets specify a 'typical' current (eg 200uA on a 16F628A) well that would make the weak pull-up 25K (based on a 5v supply).

How can you use it? If your Remote's Buttons for example are connected between the PICs pins and 0v, then you probably have an external Resistor connected between the PICs pin and Vdd. The internal weak pull-up's can save you adding that external Reistor by providing one conveniently internal to the PIC.

Different PICs handle weak pull-up's in different ways. Some WPU's can only be switched in globally across an entire port (like PortB on a 16F628), other PICs allow you to switch WPU's on a pin-by-pin basis. Like I said - not all PICs have them, and those that do might not have them on every Port or every I/O. Refer to your chosen PICs Datasheet for definitive answers.

PWM

Now with this question you have provided insufficient information for anyone to help you.

Are you speed controlling an AC or DC motor? There are different techniques for AC (and different depending on how many supply phases) or DC, and to make life more complicated there are different techniques for different kinds of motors (eg induction motor, etc etc). For some kinds of motors PWM is just unsuitable.

Likewise with your failed Lamp Dimmer... was it AC or DC or what? PWM is not suitable in all cases.