GG5, Daij, Koj, Ngrams

(a) I don't think there's a need to add to that pseudo-entry as 使わす and 遣わす are the same target, but I'll do it anyway.
(b) 遣わす is how this appears in the JEs, and it's slightly more common. I think the newspaper ranking was a mistake, and possibly based on treating it as 使う.
(c) GG5 has a kana-only additional -つかわす entry for the auxiliary verb, just showing examples: "許してつかわす. You have my pardon" and "ほめてつかわす. I commend you". In Daijirin this is a complete sense of the main entry: "（補助動詞） 動詞の連用形に助詞「て」（「で」）の付いた形に付いて，「…してやる」の意を表す。尊大な気持ちがこめられる。 「許して−・す」 「ほめて−・す」 "  I'm proposing it as an additional "uk" sense here. I'm struggling for a good gloss.

@@ -5,3 +5 @@
-<keb>使わす</keb>
-<ke_pri>news1</ke_pri>
-<ke_pri>nf02</ke_pri>
+<keb>遣わす</keb>
@@ -10 +8 @@
-<keb>遣わす</keb>
+<keb>使わす</keb>
@@ -14,2 +11,0 @@
-<re_pri>news1</re_pri>
-<re_pri>nf02</re_pri>
@@ -23,0 +20,8 @@
+<sense>
+<pos>&v5s;</pos>
+<pos>&aux-v;</pos>
+<misc>&uk;</misc>
+<s_inf>after て form, slightly pompous</s_inf>
+<gloss>to bestow (favour, etc.)</gloss>
+<gloss>to grant (e.g. pardon)</gloss>
+</sense>

See below.

Just as a point of incidental interest. When I was searching for "つかわしい"　I came across the following.

つかわした (etc.) See: 使わす

When I clicked on that I got the main entry above. When I got to that entry, the only kanji which seemed to have the reading related to "つかわした" was "遣", i.e., when based upon the kanji seen upon clicking the "examine" link. See below:-

使 [JIS] 3B48 [Uni] 4f7f [部首] 9 [教育] 3 [画数] 8  [音] シ  [訓] つか.う つか.い -つか.い -づか.い  [英]  use; send on a mission; order; messenger; envoy; ambassador; cause

遣 [JIS] 382F [Uni] 9063 [部首] 162 [教育] 8 [画数] 13 [画数] 12  [音] ケン  [訓] つか.う -つか.い -づか.い つか.わす や.る  [英]  dispatch; despatch; send; give; donate; do; undertake

I am not suggesting that the main entry above is in anyway wrong, but I am wondering if "遣" can be added to the " つかわした (etc.) See: 使わす" search aid; in order to help the searcher see potential relevance of "遣" to his or her search objective.