Issue 1:
Code Sample, a copy-pastable example if possible

In [2]: pd.Series(index=range(10))[{1:2,3:4}]
Out[2]:
1 NaN
3 NaN
dtype: float64

In [3]: pd.Series(index=range(10))[{1:2,3:4}.keys()]
Out[3]:
1 NaN
3 NaN
dtype: float64

In [4]: pd.DataFrame(index=range(10), columns=range(10))[{1:2,3:4}]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-4-5b29d5d42cf2> in <module>()
----> 1 pd.DataFrame(index=range(10), columns=range(10))[{1:2,3:4}]

~/nobackup/repo/pandas/pandas/core/frame.py in __getitem__(self, key)
2683 return self._getitem_multilevel(key)
2684 else:
-> 2685 return self._getitem_column(key)
2686
2687 def _getitem_column(self, key):

~/nobackup/repo/pandas/pandas/core/frame.py in _getitem_column(self, key)
2690 # get column
2691 if self.columns.is_unique:
-> 2692 return self._get_item_cache(key)
2693
2694 # duplicate columns & possible reduce dimensionality

~/nobackup/repo/pandas/pandas/core/generic.py in _get_item_cache(self, item)
2482 """Return the cached item, item represents a label indexer."""
2483 cache = self._item_cache
-> 2484 res = cache.get(item)
2485 if res is None:
2486 values = self._data.get(item)

TypeError: unhashable type: 'dict'

In [5]: pd.DataFrame(index=range(10), columns=range(10))[{1:2,3:4}.keys()]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-5-030f516d9637> in <module>()
----> 1 pd.DataFrame(index=range(10), columns=range(10))[{1:2,3:4}.keys()]

~/nobackup/repo/pandas/pandas/core/frame.py in __getitem__(self, key)
2683 return self._getitem_multilevel(key)
2684 else:
-> 2685 return self._getitem_column(key)
2686
2687 def _getitem_column(self, key):

~/nobackup/repo/pandas/pandas/core/frame.py in _getitem_column(self, key)
2690 # get column
2691 if self.columns.is_unique:
-> 2692 return self._get_item_cache(key)
2693
2694 # duplicate columns & possible reduce dimensionality

~/nobackup/repo/pandas/pandas/core/generic.py in _get_item_cache(self, item)
2482 """Return the cached item, item represents a label indexer."""
2483 cache = self._item_cache
-> 2484 res = cache.get(item)
2485 if res is None:
2486 values = self._data.get(item)

TypeError: unhashable type: 'dict_keys'

Problem description

I know that DataFrame.__getitem__ is a mess ( #9595 ), but I don't see why dicts and dict keys shouldn't be just considered list-likes as it happens with Series.

Expected Output

In [6]: pd.DataFrame(index=range(10), columns=range(10))[list({1:2,3:4})]
Out[6]:
1 3
0 NaN NaN
1 NaN NaN
2 NaN NaN
3 NaN NaN
4 NaN NaN
5 NaN NaN
6 NaN NaN
7 NaN NaN
8 NaN NaN
9 NaN NaN

Output of pd.show_versions()

INSTALLED VERSIONS

commit: None

python: 3.5.3.final.0

python-bits: 64

OS: Linux

OS-release: 4.9.0-6-amd64

machine: x86_64

processor:

byteorder: little

LC_ALL: None

LANG: it_IT.UTF-8

LOCALE: it_IT.UTF-8

pandas: 0.24.0.dev0+25.gcd0447102

pytest: 3.5.0

pip: 9.0.1

setuptools: 39.2.0

Cython: 0.25.2

numpy: 1.14.3

scipy: 0.19.0

pyarrow: None

xarray: None

IPython: 6.2.1

sphinx: 1.5.6

patsy: 0.5.0

dateutil: 2.7.3

pytz: 2018.4

blosc: None

bottleneck: 1.2.0dev

tables: 3.3.0

numexpr: 2.6.1

feather: 0.3.1

matplotlib: 2.2.2.post1153+gff6786446

openpyxl: 2.3.0

xlrd: 1.0.0

xlwt: 1.3.0

xlsxwriter: 0.9.6

lxml: 4.1.1

bs4: 4.5.3

html5lib: 0.999999999

sqlalchemy: 1.0.15

pymysql: None

psycopg2: None

jinja2: 2.10

s3fs: None

fastparquet: None

pandas_gbq: None

pandas_datareader: 0.2.1

Issue 2:
Should use a more intelligent algorithm than using np.random.permutation