1. What are the trends for atomic size across a period and down a group for the
main group elements?
2. Draw the following Lewis structures:
a) ammonium ion b) sulfur trioxide c) hydrogen cyanide
3. Using formal charge formula (or electronegativity differences), to determine
the following the best structure, OCS, COS or CSO.

Here's what I get  

Explanation:

1. Trends in atomic size

Atomic size tends to decrease from left to right across the Periodic Table.

You are adding one electron at a time. the electrons repel each other, so the size should increase.

You are also adding a proton to the nucleus. The additional attraction should pull the electrons closer to the nucleus.

The nuclear pull wins, so the atoms get smaller from left to right

Atomic size increases from top to bottom of a Group.

You are adding electrons to an extra shell, so the size should increase.

You are also adding protons to the nucleus, so the size should decrease.

The size of the outer shell wins, so the atomic size increases going down a Group.

2. Lewis structures

(a) Ammonium ion

N is the central atom. The N atom has the positive charge.

(b) Sulfur trioxide

S is the central atom, with a double bond to each of the three O atoms.

(c) Hydrogen cyanide

C is the central atom, with a triple bond to the N atom.

3. COS

The best structure is that of O=C=S. It has no formal charges.

The Lewis structures for the other arrangements have formal charges.