Das merke ich auch so.
This sentence is not really absolutely wrong, but suboptimal. I am not sure what you wanted to say.
Either you wanted to say »I recognize it anyway«. Then it would be better (optional, not mandatory) to replace »merken« by »bemerken«:
(a) Das bemerke ich auch so.
Or you wanted to say »I remember it anyway«. In this case it would be better (here mandatory, not optional) to insert »mir«:
(b) Das merke ich mir auch so.
In both cases »auch so« has the meaning: »without additional help«. I will omit this two words for my further analysis.
Lets have a look on
Das bemerke ich.
This is a correct and complete German sentence. It has almost the same meaning as this sentence:
Ich bemerke das.
The difference is just the word-order, and the fact what you want to emphasize. If you want to emphasize that it is you who recognizes something, then you say »Ich bemerke das«. If you want to emphasize that it is »das« (it) that is recognized (accidentally by you), then you say »Das bemerke ich«.
You must know, that in German the word-order in sentences is much more flexible than in English. In »Das bemerke ich« you have the order Object-Verb-Subject (OVS). In »Ich bemerke das« the order is Subject-Verb-Object (SVO).
Both orders are allowed, and since »ich« can not be the object (because »ich« is for sure in nominative case, but an object never can be nominative), it is in both orders clear what is the subject and what is the object.
Now let analyze
Das merke ich mir.
First of all you must learn, that »merken« in the meaning of »remember« is always reflexiv (which is not true for the english »remember«). So you always must add »mir«, »dir«, »sich«, »uns« or »euch«. And it is transitiv. So must say what you are remembering (here: das (in english: it).
But here too you can change the word-order without changing the meaning:
Ich merke mir das.
In both cases »das« is the Object that is been remembered. »Ich« is the subject (The entity that performs the act of remembering). And »mir« is the Dativ-Oject that belongs to »ich« and is necessary because merken is reflexiv.
If a verb is reflexiv and both objects stand behind the verb (like in »Ich merke mir das«), then the reflexiv-dativ-object must be placed on the 1st position and the transitiv-akusative-object comes as second. This means, that »Ich merke das wir« is wrong.
Ich arbeite auch bei hier.
This sentence is definitely wrong. The word »auch« is in english »also«. I omit it for a moment. (I am working with »Ich arbeite bei hier.«)
There are two possible ways to correct the sentence :
(a) Ich arbeite hier. (without bei) (I work here.)
(b) Ich arbeite bei diesem Unternehmen. (hier is replaced by a dative-object that represents something where people can work) (I work at this company)
Here »ich« is the subject (the entity that is working) and both »hier« and »bei diesem Unternehmen« are objects, that tell you where the subject is working.
But as said before: German has a much more flexible word-order than Englisch, so you can do the same thing as before: Let subject and object change places:
Hier arbeite ich.
Bei diesem Unternehmen arbeite ich.
Both sentences are correct and complete German sentences with the word-order OVS, and both sentences have the same meaning as their SVO-counterparts. (Only the focus of emphasis differs. It is always on the first part of the sentence.)
What about the word auch?
When you add »auch« (english also or too) to the sentence, it depends on the word-order what meaning you get. (In the next examples you always can replace »hier« by »bei diesem Unternehmen«):
1) Auch ich arbeite hier. = It's also me who is working here.
2) Ich arbeite auch hier. = I also work here. (auch/also might refer as well to the verb as to the object)
3) Ich arbeite hier auch. (correct, but not very common) = I also work here.
4) Auch hier arbeite ich. = I also work here. (auch/also only referes to the object, not to the verb)
5) Hier arbeite auch ich. = Also me is working here.
6) Hier arbeite ich auch. = Same meaning as in 2.
Add-on for 2)
Das ist meine Wohnung. Ich wohne hier. Ich arbeite auch hier.
This is my apartment. I live here. I also work here.
(auch/also referes to the verb)
Ich habe zwei Arbeitsplätze. Ich arbeite die meiste Zeit in Graz. Ich arbeite auch hier.
I have two working places. Most of the time I work in Graz. I also work here.
(auch/also referes to the object)
Explanation for 4)
This sentence has the same meaning as in the example starting with »Ich habe zwei Arbeitsplätze«. I can not mean the same as in »Das ist meine Wohnung«.
Explanation for 5)
Many other people are working here. I am one of them.