If according to my Bible translation - please correct me if it is wrong - anything a woman in niddah or a state of tumah, or 'impurity', touches or sits on becomes 'impure', can food cooked by her be eaten by others and if so, do they also become tumah?
Yes, someone who eats impure food becomes impure themselves (Rambam Shar Avot Hatumah 8:10).
However, this needs some perspective. Niddah is one kind of impurity, and another one is that of a corpse (see Numbers 19). The procedure for purifying oneself of Niddah-impurity is by using a mikvah which can and is done today regularly. The procedure for purifying oneself from corpse-impurity involves the Red Heifer (outlined in the verses there) which is not something we have available today. Thus every Jew today is already in a certain state of impurity. As such, we are not careful to not consume impure food, as we are already impure.
To clarify, even if we were all pure, one would generally only choose to avoid eating impure foods if one would have needed to remain pure later on for various sacrificial or Temple related rites. Otherwise impure foods are just as "kosher" as pure foods according to the basic letter of the law. Rambam discusses the value of food impurity at the very end of his Laws of Food Impurity (16:12):
אף על פי שמותר לאכול אוכלין טמאים ולשתות משקין טמאים, חסידים הראשונים היו אוכלין חוליהן בטהרה ונזהרין מן הטומאות כולן כל ימיהן; והן הנקראין פרושים. ודבר זה קדושה יתרה היא, ודרך חסידות שיהיה אדם נבדל ופורש משאר העם, ולא ייגע בהן ולא יאכל וישתה עימהן: שהפרישות מביאה לידי טהרת הגוף ממעשים הרעים, וטהרת הגוף מביאה לידי קדושת הנפש מן הדעות הרעות, וקדושת הנפש גורמת להידמות בשכינה, שנאמר "והתקדשתם והייתם קדושים, כי קדוש אני" (ויקרא יא,מד).
Even though it is permitted to eat impure foods and drink impure beverages, the pious men of the early generations would partake of their ordinary food in a state of ritual purity and would avoid all of the sources of impurity throughout their lives. They are called perushim.
This is an extra measure of holiness and a path to piety: to be separate from people at large, to hold oneself apart from them, not to touch them, nor eat and drink with them. For setting oneself apart leads to the purification of the body from wicked actions. Purifying one's body leads to sanctifying one's soul from wicked character traits. And the holiness of the soul causes one to resemble the Divine presence, as Leviticus 11:44 states: "And you shall make yourselves holy; and you shall be holy, because I, God, Who makes you holy, am holy."
(Translation from Chabad.org)
Even in the times of the Beis Hamikdosh (Temple) it was not mandatory not to eat food defiled by a Nidda; it was a voluntary stringency.
Generally a woman in niddah would have been in a state of confinement, perhaps only providing for herself and anyone else who may have become unclean, perhaps other daughters in the house hold? Perhaps meals were made for them, by those clean or perhaps they would provide for themselves, this decision would have depended on the individuals take on ritual cleanness, but their decisions would have been undoubtedly been affected by what time in Israel's history these events were to take place, and what unique concerns the household may have been subject to at that time. However please see: Footnote: 1. [H] (from root [H] or [H]) 'isolation', 'impurity'. A menstruant is 'isolated' from her husband and keeps away from other persons and things because, being in her 'impurity' she renders them ritually unclean if she comes into contact with them. (NIDDAH)