It seems to me you are asking about the plausibility of two different things.
First, whether most life could reproduce asexually, i.e. without combining genetic material from different individuals.
Second, whether organisms could reproduce without a dedicated reproductive stage in its life cycle, such as a foetus, egg or seed, or alternatively with a very small one. I assume the distinction you draw between an 'egg' and 'spore' is one of size.
And presumably you still want a range of organisms similar to Earth's, including plants and animals in particular.
No Genetic Exchange
From a genetic perspective, life on our planet has two mechanisms for sex. Bacteria have a subset of their genes in a separate package - a plasmid - that can be donated to another bacterium that accepts those genes.
Eukaryotes - anything with a cell nucleus - have a more organised mechanism where two cells fuse completely and the new cell has two copies of all the genes.
In both cases, a cell is accepting genes from outside. This dilutes its own existing genome, which on the face of it is bad for its existing genes, but nevertheless organisms have evolved to do so because of the great benefits that can come from new genes.
So how to stop sex evolving? One way is to make the costs even higher, and in a sense self-imposed. Suppose the greatest threat to early life on this world was viral infection, i.e. the insertion of foreign genes. Survival would depend on eliminating any genetic material from outside, and at all costs not allowing it into the host genome.
As viruses become more insidious, cells would evolve measures to destroy incoming genes (restriction enzymes, for example). Think of it as similar to rejecting a transplanted orgen. These defences would be more powerful than in our world, and would prevent sexual reproduction ever geting a start. If two cells were to fuse somehow, their defensive molecules would attack each other until one or both genomes was destroyed.
With sex out of the question, it is hard to say whether complex multicellular life could evolve. Most evolutionary biologists think not, but we won't know unless we discover other planets with strictly asexual life. So populate your world with whatever you like - except for sex-related structures such as flowers or peacocks' tails.
Sex, But Not as We Know It
There are various possibilities here, but I'll only describe one. This does involve sex in the genetic sense, but without females.
I mentioned above that eukaryotic sex involves the fusion of two cells with different genes. It is a waste of time, effort and opportunity if two cells with the same genes fuse, yet because cells divide, nearby cells will often be genetically identical. The solution is for cells to have different types. A cell of a given type can divide into two cells of the same type, but can only fuse with a cell of a different type, and therefore different genes.
We are familiar with multicellular plants and animals, which have only two mating types. In this situation, and especially when organisms become multicellular, there is a perhaps-inevitable tendency towards anisogamy. That is to say, the gametes start off all the same, trying to compromise between carrying enough nutrients to develop and being mobile enough to find a partner. But it is much more efficient for one type to grow large and well-stocked - an egg - while the other is cheap, lightweight and optimised for dispersal - sperm or pollen.
But two mating types is not the only game in town. Other organisms, fungi especially, can have more than two, sometimes dozens or hundreds. Gametes of any two different types can fuse. Because they don't know their type of partner in advance, they cannot specialise like sperm and ova.
Without egg cells, species would reproduce sexually through spores in the air or water, like mushrooms. Asexual reproduction is possible too - organisms might divide or bud in the summer, then in the autumn switch to producing spores.
This genetic system doesn't actually preclude more familiar methods of reproduction. You could have three or more types, and females would be disinclined to mate with males of their own type. Perhaps that's what the humanoids do.
Of course, this is just an outline, I have omitted many details, such as whether the haploid or diploid phase dominates the life cycle.
