Well, your PHP is gibberish, and contrary to what others are saying you CAN put an array into a database, if you STOP writing your SQL like it's still 2004 with the deprecated mysql_ functions -- you know, hence the giant red warning boxes in the manual? At least then you could axe all those variables for nothing and endless crappy 'escape' functions -- since something like PDO:repare and PDOStatement::Execute can do exactly what you are asking, dump an array into a database.
You'd also have a lot better a time of it if you had semantic markup and a form structure that... well... made sense. I mean tables for layout, inlined style, no LABEL or semantic relationship between INPUT and LABEL, and since that display state is inlined, likely no graceful degradation scripting off either. Laundry list of how not to code a form.
Likewise if the value of your option is the same as it's content, you don't need to use value... and as a USER I'd just use a text input to let people type in the blasted date, but that's because select for 30+ days and chrismas knows how many years is ANNOYING AS HELL!
Your method of indexing those elements is just asking for it to fail. Never been a fan of  and blinding hoping it works, but more so if you made your indexes be meaningful, you could just grab and insert each one the same way.
Of course, your database fields don't even correspond to the data you're shoving into the query -- see how you have fname and lname being put in, but the database only has c_name? Your database fields don't even make sense given your form! Much less the child ID -- shouldn't that be an auto-increment (probably the KEY) in the database and as such NOT even in the INSERT statement?
I'm guessing WILDLY here, but I'd approach that thus:
<legend><span>Child <span class="number"></span></legend>
SPAN is there as LEGEND are hard to style consistently cross-browser
but we want a LEGEND for semantics and accessibility...
<select name="formName[child][salutations]" id="child_Salutations">
<option value="" disabled selected>S</option>
<option value="Datin Paduka">Datin Paduka</option>
<label for="child_FirstName">First Name:</label>
<input type="text" name="formName[child][:firstName]" id="child_FirstName" />
<label for="child_LastName">Last Name:</label>
<input type="text" name="formName[child][:lastName]" id="child_LastName" />
<label for="child_DoB">Date of Birth:</label>
<input type="text" name="formName[child][:dob]" id="child_DoB" />
<label for="child_Address1">Home Address (line 1):</label>
<input type="text" name="formName[child][:address1]" id="child_Address1" />
<label for="child_Address2">(line 2):</label>
<input type="text" name="formName[child][:address2]" id="child_Address2" />
<label for="child_MobileNum">Mobile Number:</label>
<input type="text" name="formName[child][:mobile]" id="child_MobileNum" />
<label for="child_OfficeNum">Office Number:</label>
<input type="text" name="formName[child][:mobile]" id="child_OfficeNum" />
<label for="child_eMail">E-Mail Address:</label>
<input type="email" name="formName[child][:email]" />
Should be ALL you need for the form. Set the label to display:inline-block, and an elastic (em) width, with text-align:right; -- trust me on that, no table needed. that's the SEMANTIC markup for building a form PROPERLY!
See how I did "formName[child][fieldName]" -- if you make the fieldName identical to it's database counterpart, all you'd need to do for the SQL query is:
/* assumes $db is a connected PDO object */
$statement = $db->prepare('
INSERT INTO child (
userid, salutation, firstname, lastname, dob,
addr1, addr2, mobile, office, email
) values (
:userId, :firstName, :lastName, :dob,
:addr1, :addr2, :mobile, :office, :email
$_POST['child'][':userId'] = $user;
... and that's why I prefer PDO over mysqli (or the insecure mysql_ crap we were supposed to stop using the day PHP 5.1 dropped). Try that with bindParam. No "realEscapeString" sanitization nonsense needed, PDO handles that for you.
Naturally you'd want some element validation on that -- I'd probably have it work like how I do all my forms -- have the form built off a static array that includes the field type, so I could use that array to also verify the field values. Oh, and on rejection for errors, might be a good idea to re-issue the form since again, client side validation shouldn't be trusted.