About that MOSFET. What kind... is IRFZ14 ok ? (So that it doesn't heat much and waste energy.)
In what ampere MOSFET starts to show alarming temperature rise ?
The important MOSFET specification is Rds(on). This is the effective resistance between drain and source when the MOSFET is turned ON by positive gate voltage. It is usually specified at one or more values of Vgs (gate-source voltage). In your case the gate-source voltage will be somewhat less than the 555's supply voltage; assume about 9.5~10V. This is enough to saturate any MOSFET and produce a low Rds resistance.
The IRFZ14 is specified with an Rds(on) of 0.2 ohms at Vgs=10V. You can calculate its power dissipation from P = I^2 R, where:
P is power dissipation, in watts;
I is load current, in amps;
R is Rds(on), in ohms.
In your case, I=10 so I^2 is 100, and R is 0.2 ohms. Therefore P = 20 watts. The MOSFET will definitely require a heatsink. If you want to avoid a heatsink you need to use a MOSFET with a much lower Rds(on). You need to keep the power dissipation less than about 1W.
Calculating in reverse for an Rds(on) value to give 1W dissipation:
R = P / I^2
= 1 / 100
= 10 milliohms.
So you need a MOSFET that's rated for at least 10A drain current, and Rds(on) of 10 milliohms or less.
Here's a suitable MOSFET:
http://www.digikey.com/product-detail/en/IPS075N03L G/IPS075N03L G-ND/2081218
Infineon IPS075N03L, 30V, 50A, Rds(on)(max) = 7.5 milliohms, USD 0.73 for 1-up.
It may seem over-rated but it's one of the cheapest suitable through-hole parts available from Digikey.
What power(wattage) rating on 1KΩ resistor ?
Just 1/4 watt is fine.
I would like to use DPDT(15A rating) switch to reverse motor (No diode in motor is then possible... I'm right ? Diode breaks ?)
In that case, connect the diode on the MOSFET side of the reversing switch. In other words, connect the diode with its anode to the drain of the MOSFET and its cathode to the positive supply. Connect the input wires of the reversing switch across that diode, and connect the output wires of the reversing switch to the motor.
You can avoid having a large reversing switch if you drive the motor using an "H-bridge". This requires four MOSFETs instead of one. Search for H-bridge on Google or Wikipedia for more information.
