Are they all of the form `[kanji]しい` or can they also be of the form
`[kanji][kana]しい`? (`[kana]しい` can also probably be found in the case of
uncommon _kanji_.)
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i-adjectives spelling
Structure of -しい adjectives
Your question as written is more about spelling.

Looking more deeply at your intent, you could be asking whether ～しい adjectives
are always derived from 体言 or uninflecting words, or whether they are also
derived from 用言 or inflecting words.

### ～しい adjectives derived from 用言

  * _kuwashii_ , probably ultimately from ancient verb 構【く】う "to build up"
  * _urayamashii_ , from verb 羨【うらや】む "to envy, to be jealous of"
  * _misuborashii_ , from either 身【み】 or 見【み】 + 窄【すぼ】る "to be sunken in"
  * _konomashii_ from verb 好【この】む "to like, to prefer"
  * _yamashii_ from verb 病【や】む "to get sick"
  * _hoshii_ appears to be from verb 欲【ほ】る "to want, to desire"

### ～しい adjectives derived from 体言

There seem to be much fewer of these.

  * _otonashii_ from noun 大人【おとな】
  * _hisashii_ from noun 久【ひさ】
  * _hitoshii_ from number 一【ひと】
  * _nikunikushii_ from 憎【にく】憎【にく】, reduplication of the root _niku_ of verb 憎【にく】む, adjective 憎【にく】い
  * _zūzūshii_ apparently from ずぶずぶ "dead drunkenly" from ずぶ "completely wet, completely soused"

* * *

The above is by no means intended to be an exhaustive list, but rather just a
sampling to show the broad patterns. In rough summary, ～しい adjectives have
historically been formed from just about any part of speech: from verbs,
nouns, adverbs. Verb derivations appear to be the most common.
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answer
If you are asking the question from a purely orthographic aspect, the answer
is written on the government's website.

Below are excerpts from the public notice issued in 1973 named
[送り仮名の付け方](http://www.bunka.go.jp/kokugo_nihongo/sisaku/joho/joho/kijun/naikaku/okurikana/index.html).
(Underlining in the original text is converted to italic, because there is no
way to represent it due to [SE's technical
limitation](https://meta.stackexchange.com/q/117016/313522).)

* * *

> **語幹が「し」で終わる形容詞は,「し」から送る。**  
>  [ _(I-)adjectives
> whose[語幹](https://dictionary.goo.ne.jp/jn/76386/meaning/m2u/) ends in し have
> okurigana from the し._]  
>  〔例〕 著 _しい_ 惜 _しい_ 悔 _しい_ 恋 _しい_ 珍 _しい_

* * *

> **本則**  
>  活用語尾以外の部分に他の語を含む語は,含まれている語の送り仮名の付け方によって送る。（含まれている語を〔 〕の中に示す。）  
>  [ _Words that contain other words in their
> non-[活用語尾](https://dictionary.goo.ne.jp/jn/42994/meaning/m0u/) portion
> follows the contained word on where to start okurigana._]  
>  [...] _勇ま_ しい〔勇む〕 _輝か_ しい〔輝く〕 _喜ば_ しい〔喜ぶ〕  
>  [...] _頼も_ しい〔頼む〕  
>  [...] _恐ろ_ しい〔恐れる〕  
>  [...] _憎_ らしい〔憎い〕 _古_ めかしい〔古い〕  
>  [...] _男_ らしい〔男)[sic]

* * *

> **（注意）**  
>  次の語は,それぞれ〔 〕の中に示す語を含むものとは考えず,通則1によるものとする。  
>  [ _The following words are not deemed to contain each word in parentheses,
> and follows 通則1 (note: the first excerpt)._ ]  
>  明るい〔明ける〕 荒い〔荒れる〕 悔しい〔悔いる〕 恋しい〔恋う〕

* * *

> **本則**  
>  複合の語（通則7を適用する語を除く。）の送り仮名は,その複合の語を書き表す漢字の,それぞれの音訓を用いた単独の語の送り仮名の付け方による。  
>  [ _Okurigana of compounds follows (the result of) respective okurigana
> rules applied to each single constituent's kanji reading._ ]  
>  [...] 聞 _き_ 苦 _しい_ [...] 待 _ち_ 遠 _しい_ 軽々 _しい_ 若々 _しい_ 女々 _しい_

* * *

> **許容**  
>  読み間違えるおそれのない場合は,次の( )の中に示すように,送り仮名を省くことができる。  
>  [ _Okurigana can be omitted when no confusion is expected, as shown in
> parentheses._ ]  
>  [...] 聞 _き_ 苦しい（聞苦しい） 待 _ち_ 遠しい（待遠しい）

* * *

I don't think I have been formally taught about these rules, but hardly see
modern writing deviates from them anyway. Of course, the guideline assumes you
have the understanding of Japanese vocabulary as a native speaker, but that
should be made up for by trying dictionary.

One point is that a word that has etymological stem which is no longer valid
in the modern language is generally not counted as rationale to push back the
start point of okurigana. Same if the adjective have got its own kanji.

> 慌【あわ】ただしい (contains 慌てる)  
>  甚【はなは】だしい (contains 甚だ)  
>  夥【おびただ】しい (contains no living word)
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answer