divide group data base on select columns values?

Use sort_values to make sure type == 1 is the first row per group and extract them with groupby.transform('first'):

df = df.sort_values(['ts_code', 'type'])
close1 = df.groupby('ts_code')['close'].transform('first')
df['close'] = close1 / df['close']

#         ts_code  type     close
# 0     861001.TI     1  1.000000
# 1     861001.TI    20  1.101644
# 2     861001.TI    30  1.042566
# 3     861001.TI    60  0.852458
# ...         ...   ...       ...

Then pivot the type column into column headers:

out = (df.pivot(index='ts_code', columns='type', values='close')
         .drop(columns=1)
         .add_prefix('l')
         .add_suffix('d_close'))

# type       l5d_close  l20d_close  l30d_close  l60d_close  l90d_close
# ts_code
# 861001.TI        NaN    1.101644    1.042566    0.852458    0.950296
# ...              ...         ...         ...         ...         ...

To chain together, assign a ratio column before the pivot:

(df.assign(ratio=df.groupby('ts_code').close.transform('first').div(df.close))
   .pivot(index='ts_code', columns='type', values='ratio')
   .drop(columns=1)
   .add_prefix('l')
   .add_suffix('d_close'))

# type       l5d_close  l20d_close  l30d_close  l60d_close  l90d_close
# ts_code
# 861001.TI        NaN    1.101644    1.042566    0.852458    0.950296
# ...              ...         ...         ...         ...         ...

well, I don't think you need group by here as you aren't really grouping or using any aggregative function.
I think it will be easier to just create a new DF using a function

ts_codes = df.ts_code.unique()
types = [5,20,30,60,90,180,200]
ts_results = []
for ts_code in ts_codes:
    ts_result = [ts_code]
    temp = df.loc[df.tscode == ts_code]
    val_1 = temp.loc[df.type == 1]['close'].iloc[0] # to get the actual value 
    for type in types:
        val = temp.loc[df.type == type]
        if len(val) > 0:
            ts_result.append(val_1/val)
        else:
            ts_result.append(None)
    ts_results.append(ts_result)
results_df = pd.DataFrame(ts_results,coluns=['ts_code','l5d_close', 'l20d_close' …… 'l90d_close']

I didn't run the code to get the results as you didn't provide an easy way to generate your data hope this help

and sorry but sometimes the easy solution is the best (I would have move it to a function)

You can do this with pandas.DataFrame.pivot_table() (docs). As long as there's some data of each type, that column will be created.

pivoted = (
    df.pivot_table(values=["close"], index="ts_code", columns="type")
    # get rid of the first MultiIndex level
    .droplevel(0, axis=1)
    # divide type == 1 column values by every other column
    .pipe(lambda f: f[[1]].values / f.iloc[:, 1:])
    .round(2)
)

# format column names
pivoted.columns = "l" + pivoted.columns.astype(str) + "d_close"
pivoted

This returns:

type       l5d_close  l20d_close  l30d_close  l60d_close  l90d_close
ts_code                                                             
861001.TI        NaN    1.101644    1.042566    0.852458    0.950296
885933.TI        NaN         NaN         NaN         NaN         NaN
885934.TI   0.940818         NaN         NaN         NaN         NaN
885935.TI   1.056502         NaN         NaN         NaN         NaN

def get_sum_by_type(ts_code,type):
    num = df.query(f"ts_code=='{ts_code}' and type==1")['close'].sum()
    den = df.query(f"ts_code=='{ts_code}' and type=={type}")['close'].sum()
    return 

types = [5,20,30,60,90,180,200]
results = []
for tscode, type in zip(df.ts_code.uniques(), types):
    template = dict(ts_code=tscode)
    template.update({
        f"l{type_}d_close": get_sum_by_type(tscode, type ) for type_ in types
    })
    results.append(template)
goal = pd.DataFrame(results)

The only thing I see in the code is that you will need to replace the zeros for nan, because when there are no type_1 for a given ts_0, the function get_sum_by_type will return 0 due the num will be 0. You can manage the 0/0 operations inside get_sum_by_type if there are no close for a given ts_code and type