I am a newbie. I would like to kno whether the original Atmega328 on Arduino Uno, programmed with my own sketch, can be removed from an Arduino Uno board and used on my customised PCB?
Yes. Just need a few components:
10K reset pullup resistor.
0.1uF or 100nF ceramic caps:
1 to bring in DTR signal from an FTDI Basic if you plan to reprogram the '328P, or to have a serial interface for debugging
1 on the Aref pin for analog voltage reference decoupling
1 on the VCC pin
1 on the Avcc pin. Avcc also connect to Vcc.
Crystal and two 22pF caps as noted already, or a 3-pin resonator, at 16 MHz. Alternately, you can use the internal 8 MHz circuit for the clock, but the clock source fuses will need to be re-Programmed (using a Programmer).
If you will using a Reset switch, then a diode across the 10K pullup resistor (cathode to the 5V supply, anode to the Reset pin) can also prevent any high voltage glitches on the Reset signal from looking like a High Voltage programming pulse and making the chip look hung up as it waits for the programming sequence to begin.
Yes, it can. Your board will need to provide +5v and ground, a reset signal, and a crystal for the chip's programmed clock frequency (unless you reprogrammed it to use its internal clock). The power and clock signals will need filter capacitors. You can even re-program it on the board with an FTDI (USB-TTL Serial) cable.
There are lots do-it-yourself instructions to build an Arduino board, which is a good place to start, even if what you eventually want is a larger system board with an Arduino integrated into it. This is one I can vouch for; I built Mr. Alves' Version-1 as my only Uno-like board and have been using it for several years.
Yes I did it. Making the board was not so difficut but took quite some time to solder all the components the others mentioned (chrystals,capacitors, resistors and connectors. However,I found the Nick Gammon site very useful, particularly for the programming