Firstly I think you should beware of doctrines which sound similar but for different purposes.
For example, you know Newton's law of gravitation? That force is proportional to the inverse square of the distance between two objects? I once read an SF story in which characters, who had "lapsed into a pre-technological culture marked by superstition"), when they read this law, assumed that it was talking about "love" -- i.e. that people are more attracted to each other when they're closer together!
I think that's an example of one law (or doctrine) sounding the same as another, but actually being very different.
Without trying to read about and understand "Spread mind" I can't assess whether it's in any way, nor whether it's fundamentally, similar to Buddhism.
Now, looking only at the surface meaning of the words you quoted ...
Consciousness is the object one is conscious of
I think that one of the Buddhist doctrines suggests there is ...
- Sense object (e.g. the thing seen)
- Sense organ (e.g. the eye)
- Sense consciousness
- Contact between the above
... and that all of these are necessary for there to be a sight. Similarly for the all 6 senses ("6" because "mind" is treated as one of the senses ... the mind is a sense organ which perceives "mind objects" e.g. ideas).
See e.g. saḷāyatana for further details.
A physical entity exists if and only if it is the actual cause of something else
I guess this reminds me of Heisenberg, i.e. that you can't be aware of something (so it might as well not exist) unless it has an effect on (and incidentally is affected by) something observable.
Maybe it also reminds me of light cones.
In a Buddhist context I suppose I'd understand it to mean we should discount many things as unreal (or not existing) because they don't cause something else. For example, if I'm worried about the monster under my bed and ... wait for it ... I'm not eaten ... I'm conscious of breathing ... then the "monster" didn't actually cause anything and thus doesn't exist as a physical entity.
Buddhism has a lot to say and not all of it agrees with the quoted statement: for example it might say that actions or intentions cause things; or that physical entities are maybe not "entities", but are mere "aggregates" (and temporary aggregates) of other things.
Another fundamental doctrine is that anything which exists because it's caused (or when the conditions exist for its existence) will cease when its cause no longer exists (or when the conditions for its existence cease).
Buddhism may encourage us to try to stop causing more and more (which is called Saṃsāra), and to attain Nirvana (which is also called the "unconditioned" or uncaused, "timeless", and so on).
The past is not defined until it produces an effect, but once it does, the past has been defined since it occurred originally.
I don't know; Buddhism has some things to say about the past ... that what happens now depends partly on what happened previously ... but perhaps it isn't (or sometimes tries to encourage us not to be) overly interested in that.
To become "attached" to something past is a cause of suffering (if I love someone and become attached to them and they die, for example, that's kind of unfortunate; or conversely if I fight with someone and become attached to that fight and carry it around with me for the rest of my life, then that's too bad too).
Perhaps Buddhism is more interested in being mindful of (or in) the present, and the future.
Buddhism does suggest that there's been a lot of past (ever so many lifetimes), perhaps for salutary reasons.
Its doctrines about karma (actions sometimes have an immediate effect, sometimes a later effect) are barely comprehensible IMHO.