Your observation is right.
1. In females( having XX mammalian germ cells), Oogenesis starts with the process of developing primary oocytes, which occurs via the transformation of oogonia into primary oocytes, a process called oocytogenesis. Oocytogenesis is complete either before or shortly after birth.(1)
2. The "germ cells" are called oogonia. Ovum is not a direct product of meiosis I, the oocyte forms a primary oocyte in meiosis I, which undergoes meiosis II after fertilization to give an ovum.
The ootid is the immature ovum formed shortly after fertilization, but before complete maturation into an ovum. Thus, the time spent as an ootid is measured in minutes. 860
....(2)
(In oogenesis, the ootid doesn't really have any significance in itself, since it is very similar to the ovum. It matures into an ovum.)
This diagram sums it up very well:
Oogenesis in Eukaryotic Cells.(A) oogonium where the mitotic division occurs (B) differentiation and meiosis I begins (C) primary oocyte (D) meiosis I is completed and meiosis II begins (E) secondary oocyte (F) first polar body (G) ovulation must occur and the presence of the sperm penetration (fertilization) induces meiosis II to completion (H) ovum (I) second polar body ...(3)
1. It is commonly believed that, when oocytogenesis is complete, no additional primary oocytes are created, in contrast to the male process of spermatogenesis, where gametocytes are continuously created.
1. In males, again, as you say, Spermatogenesis is the process by which haploid spermatozoa develop from germ cells in the seminiferous tubules of the testis. The germ cells here are the spermatogonia. But here, initiation of spermatogenesis occurs at puberty. So, males start producing sperm when they reach puberty, which is usually from 10-16 years old.(4)
(The process is almost similar to oogenesis, I would recommend you to start with the wikipedia page if you want to understand this in detail.)
Take away points:
* The first haploid cell formed from a diploid germ cell is not an ovum/spermatogonia.
* Ovum is formed after fertilization, whereas sperms are formed at puberty.
* Oogenesis starts after birth, whereas spermatogenesis starts at puberty.
1- https://en.wikipedia.org/wiki/Oogenesis
2- https://en.wikipedia.org/wiki/Immature_ovum#Ootid
3-https://upload.wikimedia.org/wikipedia/commons/1/1a/Oogenesis.svg
4- https://en.wikipedia.org/wiki/Spermatogenesis 860