Maybe, it depends on the type of processor, other hardware and software.
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Yes.
That is completely dependant on which games you wish to play. Chances are you will need a faster processor to be able to play games such as Gears of war 2 which requires a minimum of 2.4 Ghz. Unreal tournament 3 - 2.8 Ghz, Bioshock - 2.4, C&C3 - 2.4. You can play Portal though: It only has 1.7 Ghz minimum requirement. basically your not going to be able to play much with a 1.8 Ghz processor and even if you do, the games you play will probably have to be set to the lowest graphics settings and will still lag like crazy.
To increase the clock speed of your CPU, you need to either look into overclocking (which is dangerous) or buying a new processor (which will cost anywhere from $40 to over $1000).
Yes it can. I've done it plenty of times (my computer uses a 1.8GHz dual-core). I've played UT2004 and Need for Speed Most Wanted fine on it. Mind you, if your computer has a 1.6GHz processor, increase the RAM to the maximum supported, it really helps.
The Acer Aspire One does not meet the system requirements for The Sims 3. In particular, the processor is too slow (a 1.6 GHz Atom processor vs. a 2.0 GHz Pentium 4). Most models also do not include enough storage space to store The Sims 3 effectively (at least 6 GB of free memory are needed) I suggest that you get an Apple Mac Pro, it will DEFINATLY Run Sims 3, I have one. It is on the pricey side . but it is well worth it!