Generalisation while often is a very useful tool at the zeroth approximation level, – that is crude, very crude, barely resembling the truth, – is a temptingly dangerous game to play. It often boils down complicated concepts beyond the point of usefulness and leads to wrong conclusions.
Generalisations are oversimplifications.
An example for this is the ever so annoying inclusion of d orbitals into hybridisation schemes. This was a result from the post rationalisation of VSEPR theory with molecular orbitals. It has been disproved many times, yet it still is used as a common explanation in textbooks. It is a myth that continues to live, and live, and live...
Another example for generalisation taken too far is resonance. The concept most often employed, yet understood so little about it; especially why it is neccessary in the first place. As a result we hear phrase like "most stable resonance structure", which are complete garbage.
As such, while making generalisations you might not yet realise what damage that may cause later. Some concept simply are complicated and should not be broken down further.
It is quite common to draw reaction mechanisms with Lewis structures and electron pushing arrows. The problem with these is the extremely simplified nature of these drawings. Molecules are (usually) not planar, and yet we ignore this for the purpose of representation and depiction. A picture may sometimes be worth a thousand words. However, another, probably worse, problem with these schemes is the depiction of discrete electron pairs; a contributing factor to the resonance problem mentioned above.
When using these mechanisms it is always implied, that these are proposals, simplified to highlight certain aspects of a reaction.
Let's analyse your statements a little and see where you might derail.
I claim that negative charge on phenoxide ion first ALWAYS delocalises onto the ring and then attacks through carbon atom (like in Reimer Tienman reaction).
That statement has already one big problem, it's wrong. The charge in the phenoxide ion is never localised. The electronic structure of a molecule will always adapt much more easily and fast than any given change in the molecular geometry. When phenoles are deprotonated, while the hydron leaves, the electronic structure instantaneously adapts.
You are thinking in terms of discrete resonance structures, which simply do not exist. The negative charge is delocalised. That's it. The corresponding observable is the electron density, which is concentrated at certain positions due to the excess electron. In the approximation of molecular orbital theory, this can be partially explained with the HOMO and lower orbitals. In the context of valence bond theory we need to employ resonance, i.e. the superposition of various electronic structures that feature localised electron pairs. Both representations are approximations, but currently our best way to understand complicated mechanisms.
The way how molecules react with each other depends on many things. The product which is formed depends on a fragile system of well balanced energy levels. You need to understand, that molecules react in all possible ways, but only the most stable products will eventually be retained.
In that regard you statement is also wrong, the phenoxide ion is a nucleophile, it will act through every position with increase electron density, most likely through the oxygen though.
This happens because negatively charged carbon atom is less electronegative and hence a better nucleophile than a negatively charged oxygen atom.
The pure notion of better or worse nucleophiles is highly dependent on the context. Just because formed carbon-carbon bonds tend to be a little more stable than the carbon-oxygen bonds, it is not useful to generalise that. I also highly doubt the mechanism presented on Wikipedia for the Reimer–Tiemann reaction is complete enough. As has been stated before, this is not a clean reaction, hinting at a variety of semi-stable intermediates.
But a normal lone pair like that on aniline or phenol attacks by itself without delocalisation (as in Schotten Bauman reaction). This is because delocalised resonance structures have a formal positive charge on the more electronegative oxygen/nitrogen and are thus less stable.
I don't quite understand where you are going with that, but the lone pair of nitrogen in aniline certainly has overlap with the aromatic system. In general amines and phenols are quite alright nucleophiles. There are other factors determining why they react the way they do.
Your statement suffers from the most-stable-resonance-structure-syndrome, i.e. you take resonance structures much too seriously. Please see: What is resonance, and are resonance structures real? If there is resonance, then this effect is always stabilising, because otherwise it would adopt a molecular structure where resonance would not be possible (compare cycloocta-1,3,5,7-tetraene).
Additionally formal charges are exactly what they are called: formal. There is little to no truth to them other than keeping track of all the electrons.
One of the most important things is also to realise that stability always is a relative concept. More often than not it highly depends on the chemical environment, if an intermediate is "stable" and if it would be more "stable" than another intermediate.
as a high school level student, you will learn a lot of useless or even wrong stuff. Some concepts are still taught even though they are known to be wrong. Some concepts are often not correctly understood by teachers themselves. Even at the university level you will encounter hardliners who teach chemistry like it was still the 20th century. Unfortunately that can't be changed (in the immediate future).
However, critical thinking is the way to gain knowledge. Unfortunately that means letting go of generalisations. Many things are much more complicated that they appear at first sight, only a detailed look will yield a better understanding. And once you have obtained a deep and fundamental knowledge, you won't need these generalisations or oversimplifications.