Row of natural numbers
CJam, 78 bytes
r_A,s-&quot; e . .e&quot;S/\a#[SSS&quot;'./~'e/~i1$,-'e\]s&quot;0]=~~_i:Q\Q=Qg&amp;/
s,:L{;QAL(:L#9L*(*)9/-_1&lt;}g(L)md_)p\AL#+_ps=

The program is 104 bytes long and qualifies for the bonus.
The newline is purely cosmetic. The first line parses the input, the second generates the output.
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Idea
For any positive integer k, there are 9×10k-1 positive integers of exactly k digits (not counting leading zeroes). Thus, if we concatenate all of them, we obtain an integer of 9×n×10k-1.
Now, concatenating all integers of n or less digits yields an integer of

digits.
For a given input q, we try determine the highest n such that the above expression is smaller than q. We set n := ⌈log10q⌉-1, then n := ⌈log10q⌉-2, etc. until the desired expression becomes smaller than q, subtract the resulting expression from q (yielding r) and save the last value of n in l.
r now specifies the index in the concatenation of all positive integers of l+1 digits, which means that the desired output is the r%(l+1)th digit of the r/(l+1)th integer of l+1 digits.
Code (input parsing)
r_          e# Read from STDIN and duplicate.
A,s-        e# Remove all digits.
&quot; e . .e&quot;S/ e# Push [&quot;&quot; &quot;e&quot; &quot;.&quot; &quot;.e&quot;].
\a#         e# Compute the index of the non-digit part in this array.

[SSS&quot;'./~'e/~i1$,-'e\]s&quot;0]

            e# Each element corresponds to a form of input parsing:
            e#   0 (only digits): noop
            e#   1 (digits and one 'e'): noop
            e#   2 (digits and one '.'): noop
            e#   3 (digits, one '.' then one 'e'):
            e#     './~    Split at dots and dump the chunks on the stack.
            e#     'e/~    Split the and chunks at e's and dump.
            e#     i       Cast the last chunk (exponent) to integer.
            e#     1$      Copy the chunk between '.' and 'e' (fractional part).
            e#     ,-      Subtract its length from the exponent.
            e#     'e\     Place an 'e' between fractional part and exponent.
            e#     ]s      Collect everything in a string.
            e#   -1 (none of the above): push 0

~           e# For s string, this evaluates. For 0, it pushes -1.
~           e# For s string, this evaluates. For -1, it pushes 0.
            e# Causes a runtime exception for some sorts of invalid input.
_i:Q        e# Push a copy, cast to Long and save in Q.
\Q=         e# Check if Q is numerically equal to the original.
Qg          e# Compute the sign of Q.
&amp;           e# Logical AND. Pushes 1 for valid input, 0 otherwise.
/           e# Divide by Q the resulting Boolean.
            e# Causes an arithmetic exception for invalid input.

Code (output generation)
s,:L     e# Compute the number of digits of Q and save in L.
{        e# Do:
  ;      e#   Discard the integer on the stack.
  Q      e#   Push Q.
  AL(:L# e#   Push 10^(L=-1).
  9L*(   e#   Push 9L-1.
  *)     e#   Multiply and increment.
  9/     e#   Divide by 9.
  -      e#   Subtract from Q.
  _1&lt;    e#   Check if the difference is non-positive.
}g       e# If so, repeat the loop.
(        e# Subtract 1 to account for 1-based indexing.
L)md     e# Push quotient and residue of the division by L+1.
_)p      e# Copy, increment (for 1-based indexing) and print.
\AL#+    e# Add 10^L to the quotient.
_p       e# Print a copy.
s        e# Convert to string.
2$=      e# Retrieve the character that corresponds to the residue.