Can FF3 and FF4 run separately on same computer?

YES! Any of the versions of Filter Forge are totally independent and you can all the versions if you would want in the same computer and they will be like different applications, also the same if you it as a plugin, will have each one it´s own plugin separate.

Any new update of filter forge will overwrite any of the previous version ONLY IF they have the same number, so FF 3.0.15 will be installed over 3.0.14, but 4.0.15 would never install over 4.0.14

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(apparently there is no upgrade option from the Professional to the Basic edition)

Going from Professional to Basic edition is NOT an upgrade, is an downgrade of edition although is an upgrade of version

Well, you can ask to the customer support if they could allow you to have a downgrade from FF 3.0 Professional to FF 4.0 Basic.

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if they could allow you to have a downgrade from FF 3.0 Professional to FF 4.0 Basic.

No, this is not allowed. However, as for today, Basic 4.0 is offered for only $44 — any upgrade option from the Professional Edition will be more expensive.

For me there is an important difference between Basis, Standard and Professional, and is the render speed, as only the Professional version allows you have the multicore optimization so it can run as fast as possible, because on Basic and Standard it will be more slower as it will ONLY use just ONE core and so it will reduce the perfomance.

You already have FF 3.0 Professional so you are already using the fastest version and so you are used to get the perfomance of this version, and changing to the Basic from Professional will maybe make you feel that is more slower.

I can´t tell how much slower it will become.

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Actually, I only use FilterForge once in a blue moon to edit a family photo

Maybe if you use it little you will not care probably for taken more time to do the same with FF 4.0.

The only reason I was thinking of buying it was the sale price (and it being less expensive than an upgrade from FF3 Professional to FF4 Professional).

The other reason is that you will be able to use FF 4.0 filters that you can´t use with FF 3.0, maybe you can keep using FF 3.0 for the FF 3.0 filters and below as it is faster, and then use the Basic FF 4.0 only for filters that are for FF 4.0.

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Basic and Standard it will be more slower as it will ONLY use just ONE core

Sorry I made a mistake, and this is not true, as they will support and use ALSO dual core processors.

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basic version can't handle bitmaps larger than 3000 x 3000

OH, yes, this is something also very important for me, although I did not put it as a reason because it depends totally on what kind of works and image you want to do.