1. Can anyone Find The Critical Maximum Clock for other X1k series core as well .
There are no such thing as critical max clock, every graphics card overclock diffrently, even if you bought two identical cards at the same time both card is diffrent from each other in terms of core production date and memory.

2. Do Overclocking Ability of a graphic card is limited by its Graphic card Board ( Like Processors on certain motherboard ...... Limits to most 3.8 to 4.2 max clock )
Overclocking I think didnt effect much from motherboards but it did effect from PSU (at least at the high-end segment) my 450W PSU struggle to give enough power to my X1800GTO. The memory timing and voltage on the card also play important role in overclocking the memory

3. Can a Overclocked Low end Graphic card out perform the higher end graphic card ( Like my case , X1300 series 450mhz to X1300PRO series 600MHz) across the same core and save money ? Assume the Memory is overclock as well .
X1300 to outperform what? X1600? Probably yes or not because like memory bandwidth and fill rate (X1300 and X1600 share the same amont of TMU and ROP, but the latter have 3x pixel shader,ring bus memory, twice Z-Compare unit) dont even think that X1300 can beat X1800 or X1900s


4. it seems that 700MHz is the Manufacture set maximum core speed for R520 Family core . (RX1800 XT PE R520 @ 695MHz) Is that true that All X1k series graphic Card cannot reach the speed as fast a current computers ? Or they want to save the price to use BIG heat SINKS for Cooling ?
Thats not true, this is because at some point the graphics core is just give a little bit performance boost above that speed but expell tons of heat and uses lots of power. I think manufacturers test their X1800 series and found out that above 700MHz is just not worth it if heat and power consuption comes to the equation

I think I saw somewhere that X1800 hits the 1GHz barrier but it uses Liquid nirogen I believe

My X1800GTO at 1.1V overclocks to 540MHz, 1.2V 600MHz above that I didnt dare to try anymore since I dont have sufficent power (last time I try 1.3V 661MHz). The memory stock 1.9V goes up to 621MHz and 2.2V 711MHz and thats with Samsung BC20 memory (2ns)

I knew I must be wrong about some of it. Especially the critical clock one. I still dont understand it though. My X1800GTO is perfectly stable at 1.2V at 612MHz on 3DMark06 but it failed in CoD2 even at 607MHz it just hang in the middle of the game, so what is the critical clock?

The graphics PCB also play important roles in overclocking, some manufacturers design their own PCB like Galaxy and Palit to overclock higher.

Now against the core family, the X1300 can outperform X1300Pro if heavily overclocked (assume they have same PCB and memory) but the MyperMemory cant outperform it because lacks of memory bandwidth