For the first part of the problem, all you need is an IF field, coded along the lines of:
{IF«LName2»<> "" "«LName2» «FName2» «Cell2» «Bday2» «Anniv»"}
plus whatever other formatting & conditional text might be associated with those mergefields.

As for the images, you need to embed the relevant mailmerge field in an INCLUDEPICTURE field. However, there are some issues with this that make the process less straightforward than one might expect. For example, when embedding a mailmerge field in an INCLUDEPICTURE field for the purpose of merging graphics:
1. the file paths to the fields need to have the separators expressed as '\\' or '/' instead of the usual '\';
2. the pictures usually won't show until you refresh the fields (eg Ctrl-A, then F9) in the output document after completing the merge; and
3. even after updating the images, they remain linked to the image files, which can be an issue if you later delete the image or you need to send the merged output to someone else.

The following field construction addresses all three issues (i.e. you don't need to do anything special to the paths, or refresh the fields, and they'll no longer be linked to the source files):
{IF{INCLUDEPICTURE {IF TRUE "C:\Users\My Document Path\Pictures\«Image»"} \d} {INCLUDEPICTURE {IF TRUE "C:\Users\My Document Path\Pictures\«Image»"} \d}}
or:
{IF{INCLUDEPICTURE {IF TRUE "C:\Users\My Document Path\Pictures\{MERGEFIELD Image}"} \d} {INCLUDEPICTURE {IF TRUE "C:\Users\My Document Path\Pictures\{MERGEFIELD Image}"} \d}}
After running a mailmerge coded this way, you'll have the correct, unlinked image for each record.

This form of field construction can be very useful where the filepath for the images is held in the mailmerge data source, in which case you could use:
{IF{INCLUDEPICTURE {IF TRUE "«FilePath»\«Image»"} \d} {INCLUDEPICTURE {IF TRUE "«FilePath»\«Image»"} \d}}
or:
{IF{INCLUDEPICTURE {IF TRUE "{MERGEFIELD FilePath}\{MERGEFIELD Image}"} \d} {INCLUDEPICTURE {IF TRUE "{MERGEFIELD FilePath}\{MERGEFIELD Image}"} \d}}

Note1: You need a path separator between the filepath mergefield and the image mergefield. If that separator is included in the source data, it can be omitted from the field above construction but leaving it there has no adverse effects
either.

If you can be sure the pictures will always be in the same folder as the mailmerge main document, you can incorporate a FILENAME field thus:
{IF{INCLUDEPICTURE {IF TRUE "{FILENAME \p}\..\{MERGEFIELD Image}"} \d} {INCLUDEPICTURE {IF TRUE "{FILENAME \p}\..\{MERGEFIELD Image}"} \d}}
or:
{IF{INCLUDEPICTURE {IF TRUE "{FILENAME \p}\..\«Image»"} \d} {INCLUDEPICTURE {IF TRUE "{FILENAME \p}\..\«Image»"} \d}}

If the path data are included with in the image field, you can use:
{IF{INCLUDEPICTURE {IF TRUE «Image»} \d} {INCLUDEPICTURE {IF TRUE «Image»} \d}}
or:
{IF{INCLUDEPICTURE {IF TRUE {MERGEFIELD Image}} \d} {INCLUDEPICTURE {IF TRUE {MERGEFIELD Image}} \d}}

For what it's worth, *provided* the path has the separators expressed as '\\' or '/', you can retain the links by omitting the all-encompassing IF test and the images will display correctly without the need to refresh the fields after completing the merge. For example:
{INCLUDEPICTURE {IF TRUE "C:\\Users\\My Document Path\\Pictures\\«Image»"} \d}

Note2: The field brace pairs (i.e. '{ }') for the above example are all created in the document itself, via Ctrl-F9 (Cmd-F9 on a Mac); you can't simply type them or copy & paste them from this message. Nor is it practicable to add them via any of the standard Word dialogues. Likewise, you can't type or copy & paste the chevrons (i.e. '« »') - they're part of the actual mergefields, which you can insert from the mailmerge toolbar. The spaces represented in the field construction are all required.

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]