Ég er laus á miðvikudag.

In this sentence laus means free / available (as in having no plans). It can also mean loose in other contexts (e.g., something not fastened), but with people + schedules it very commonly means available.

• Ég = the 1st person singular pronoun I (nominative case).
• er = the 1st person singular present tense of vera (to be).
  So Ég er … is the standard way to say I am ….

Predicate adjectives in Icelandic normally agree with the subject’s gender/number/case. With ég, speakers typically use the form that matches their natural gender. Conveniently, the nominative singular forms are:

• masculine: laus
• feminine: laus
• neuter: laust

So for most speakers the sentence stays Ég er laus … (male and female look the same here). laust would not be used with ég in normal speech.

á is the common preposition for a specific day (similar to English on):

• á miðvikudag = on Wednesday (one specific Wednesday)

Other prepositions exist, but á + day is the basic, most natural choice for this meaning.

The dictionary form is miðvikudagur (nominative singular). After á in this time expression, Icelandic uses the accusative, and the accusative singular is miðvikudag (dropping the nominative -ur).

Here á takes the accusative because it’s used for a point in time (on Wednesday).
But á does not always take accusative: it can take different cases depending on meaning (for example, with location it often takes dative). So you learn á + accusative specifically for this kind of time expression.

In Icelandic, days of the week are not normally capitalized, so it’s miðvikudag, not Miðvikudag (unless it begins a sentence or is in a title with special capitalization rules).

Yes.

• á miðvikudag = on Wednesday (neutral, general)
• á miðvikudaginn = on the Wednesday (more specific/pointing to a particular Wednesday, often the coming/known one in context)

Both can be correct; the definite form often feels a bit more specific.

Use the plural: á miðvikudögum = on Wednesdays (as a regular occurrence).
That’s a common way to express a repeated schedule.

You can move it for emphasis:

• Ég er laus á miðvikudag. (neutral)
• Á miðvikudag er ég laus. (emphasizes Wednesday)

Both are natural; Icelandic word order is flexible, but the verb is typically in the second position in main clauses.

A careful, learner-friendly guide:

• Ég: the g is not a hard g; it’s closer to a soft sound (often like a y-ish/glide).
• miðvikudag: ð is like the th in this (voiced).
• Stress is typically on the first syllable of words: MIÐ-viku-dag.

(Exact pronunciation varies by dialect and speaking speed.)