The primary meaning of the verb иметь is “to own, possess.” It's a fairly straightforward first conjugation verb:

The owner goes in the nominative case, and the thing owned goes in the accusative case:

Although all the sentences above are perfectly grammatical, I should point out that using иметь for “to own/have” is stylistically marked. It's more formal, higher style, and sometimes more emphatic, than the “у кого есть” construction, so don't automatically assume it's the best way to say “to own.” Soon we'll discuss the overlap between иметь sentences and «у кого есть» sentences.

The second meaning of что is “that” in the sense of “Mama said that she's going to whup your ass.” In other words, it is a conjunction that joins an introductory sentence to a bit of indirect speech:

The Russian word for ‘what’ is что. Although it is written with the letter ч, the nominative/accusative form of the word is most commonly pronounced [што]; in the other cases we do pronounce ч as ч. It occurs in all six cases:

Notice that the only difference between the prepositional and instrumental forms is the двоеточие “double dots” over the prepositional form.¹ Remember that the Russians usually do not usually write the double dots, so context will have to tell you how to pronounce those forms. Some sample sentences:

Somewhere in school every American is taught the rule “never end a sentence with a preposition.” For English it's an assinine rule that has no reasonable justification in the living language.² However, for Russian the rule is real and alive. It's not an artificial rule, as in English, but rather a subconscious part of the living language: no Russian will ever end a sentence with a preposition, not even accidentally. So whenever you are translating a question from English to Russian, and the question ends with a preposition, you need to move that preposition to before its object and then translate. Thus:

Other examples:

Notice in the last example we can leave the preposition out of the response in English, but in Russian you must retain the preposition to justify the case of памятник.

¹ The double dots symbol is often called a diaeresis or an umlaut. The former is theoretically used to indicate that a vowel is pronounced as a complete vowel (not a diphthong) when preceded by another vowel with which it might blend. The latter is theoretically used to indicate that vowel is fronted. Since neither of those instances prevails in the е/ё distinction, “double dots” is a sensible name for the symbol.

² Of course, one can't mention this rule of English without mentioning Winston Churchill's famous definition: “A preposition is a word you can't end a sentence with.” I actually doubt that Churchill said it, but it's too fun not to mention.

Бежать is the determinate (unidirectional) form of the verb бегать “to run.” It is one of the four most irregular verb stems in the Russian language:

Бежать is more specialized than бегать in that it usually talks about motion in progress at a particular time:

Although the verb does mean “to run,” it's actually used in conversation more often to mean “to take a quick trip” or “to be moving quickly” instead of literally running. The same is true for the English verb “to run” as well, of course.

The verb is also used in the sense of “to precede prematurely”:

And of course the verb is also used in the sense of “to flee”. Although in English the thing you flee from can be a direct object (“We fled Cuba in 1965”) or the object of the preposition ‘from’ (“We fled from Cuba in 1965”), in Russian the thing you flee from cannot be a direct object; it must be the object of the prepositions из/с/от followed by the genitive case:

Бегать is the most generic word in Russian that means “to run.”

Running… nowadays in the lazy West we often run in order to lose weight. That actually makes sense:

It's not usual for a person to regularly run from one place to another, but in such atypical circumstances it is possible to conceive of someone doing such a thing:

The verb is also used to describe the motion of someone running around a place with no set goal or direction, e.g. walking around a neighborhood for pleasure:

Last but not least, the verb is used to indicate a single round-trip in the past. It's not typical in this usage, but still grammatically possible: