Well no, of course iWeb won't be installed on your new MacBook Pro, because iWeb has not shipped on new Mac's for quite sometime now.
If you have your old installation CD's from your old Mac, then you can install iWeb on your new Mac or use the migration assistant.
iWeb is an application and if you have it, yes, you can still use it, but no Apple has not supported iWeb for a long time now. Not since MobileMe closed at the end of June last year.
No, iWeb is not being replaced by EasyWeb as you put it. EasyWeb is being developed by Rage software, which is a totally different company as perhaps a suitable replacement app for iWeb, but it is not by Apple and also, when it is released you will have to purchase hosting with Rage if you want to use the app. You won't just be able to purcahse the app on its on - in the first instance it will be tied to Rage hosting.
If you have iWeb on your old Mac, then transfer it to your new Mac and continue to use it. You could upgrade to iWeb 09 if you wanted, as it states that you have iWeb 08? However, you will have to purchase this from Amazon and get the iLife 11 or iLife 09 boxed set which contains iWeb 09, which is the most up to date version.
It might be better to do this as iWeb 09 is likely to be more compatible with Mountain Lion than iWeb 08.
Essentially, yes if you have iWeb on your Mac then you can still use it, but it is not supported by Apple any longer and has not been for sometime now.
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